[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/1255#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/1255","headline":"\u5b89\u5b9a\u66f2\u7dda – Wikipedia","name":"\u5b89\u5b9a\u66f2\u7dda – Wikipedia","description":"\u5b89\u5b9a\u66f2\u7dda\uff08\u3042\u3093\u3066\u3044\u304d\u3087\u304f\u305b\u3093\u3001\u82f1: stable curve\uff09\u3068\u306f\u3001\u4ee3\u6570\u5e7e\u4f55\u5b66\u306e\u7528\u8a9e\u3067\u3001\u5e7e\u4f55\u5b66\u7684\u4e0d\u5909\u5f0f\u8ad6\u306e\u610f\u5473\u3067\u6f38\u8fd1\u7684\u306b\u5b89\u5b9a\u306a\u4ee3\u6570\u66f2\u7dda\u306e\u3053\u3068\u3067\u3042\u308b\u3002 \u3053\u306e\u6761\u4ef6\u306f\u3001\u5b8c\u5099\u9023\u7d50\u66f2\u7dda\u3067\u3042\u3063\u3066\u3001\u305d\u306e\u7279\u7570\u70b9\u306f\u901a\u5e38\u4e8c\u91cd\u70b9\u306e\u307f\u3067\u3042\u308a\u3001\u304b\u3064\u81ea\u5df1\u540c\u5f62\u7fa4\uff08\u82f1\u8a9e\u7248\uff09\u304c\u6709\u9650\u7fa4\u3067\u3042\u308b\u3053\u3068\u3068\u540c\u5024\u3067\u3042\u308b\u3002\u81ea\u5df1\u540c\u5f62\u7fa4\u304c\u6709\u9650\u3067\u3042\u308b\u3068\u3044\u3046\u6761\u4ef6\u306f\u3001\u7b97\u8853\u7a2e\u6570\u304c1\u3067\u306f\u306a\u304f\u3001\u304b\u3064\u5168\u3066\u306e\u975e\u7279\u7570\u6709\u7406\u66f2\u7dda\u6210\u5206\u304c\u4ed6\u306e\u6210\u5206\u3068\u5c11\u306a\u304f\u3068\u30823\u70b9\u3067\u4ea4\u53c9\u3059\u308b\u3068\u3044\u3046\u6761\u4ef6\u306b\u7f6e\u304d\u63db\u3048\u3089\u308c\u308b[1]\u3002 \u81ea\u5df1\u540c\u5f62\u7fa4\u306b\u6709\u9650\u7fa4\u3067\u306f\u306a\u304f\u7c21\u7d04\uff08reductive\uff09\u7fa4\u3092\u8a31\u3057\uff08\u3053\u308c\u306f\u9023\u7d50\u6210\u5206\u306b\u30c8\u30fc\u30e9\u30b9\u3092\u8a31\u3059\u3068\u3044\u3046\u6761\u4ef6\u3068\u540c\u5024\u3067\u3042\u308b\uff09\u3001\u307b\u304b\u306f\u540c\u69d8\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u3082\u306e\u3092\u534a\u5b89\u5b9a\u66f2\u7dda\uff08semi-stable curve\uff09\u3068\u3044\u3046[\u8981\u51fa\u5178]\u3002\u3042\u308b\u3044\u306f\u3001\u975e\u7279\u7570\u6709\u7406\u6210\u5206\u304c\u4ed6\u306e\u6210\u5206\u3068\u5c11\u306a\u304f\u3068\u30823\u70b9\u3067\u4ea4\u53c9\u3059\u308b\u3068\u3044\u3046\u6761\u4ef6\u3092\u3001\u5c11\u306a\u304f\u3068\u30822\u70b9\u3067\u4ea4\u53c9\u3059\u308b\u3068\u3044\u3046\u6761\u4ef6\u306b\u7f6e\u304d\u63db\u3048\u305f\u3082\u306e\u3067\u3042\u308b\u3002 \u540c\u69d8\u306b\u3001\u6709\u9650\u500b\u306e\u6a19\u70b9\u4ed8\u304d\u66f2\u7dda\u304c\u5b89\u5b9a\u3068\u306f\u3001\u5b8c\u5099\u9023\u7d50\u3067\u3042\u3063\u3066\u7279\u7570\u70b9\u306f\u901a\u5e382\u91cd\u70b9\u306e\u307f\u3092\u6301\u3061\u81ea\u5df1\u540c\u5f62\u7fa4\u304c\u6709\u9650\u3067\u3042\u308b\u3053\u3068\u3092\u3044\u3046\u3002\u4f8b\u3048\u3070\u3001\u6955\u5186\u66f2\u7dda\uff08\u7a2e\u65701\u306e1\u6a19\u70b9\u4ed8\u304d\u975e\u7279\u7570\u66f2\u7dda\uff09\u306f\u5b89\u5b9a\u3067\u3042\u308b\u3002 \u8907\u7d20\u6570\u4f53\u4e0a\u3067\u306f\u3001\u9023\u7d50\u306a\u66f2\u7dda\u304c\u5b89\u5b9a\u3067\u3042\u308b\u3053\u3068\u3068\u3001\u5168\u3066\u306e\u7279\u7570\u70b9\u3068\u6a19\u70b9\u3092\u9664\u304f\u3068\u5404\u6210\u5206\u306e\u666e\u904d\u88ab\u8986\u304c\u5358\u4f4d\u5186\u677f\u3068\u540c\u578b\u306b\u306a\u308b\u3053\u3068\u306f\u540c\u5024\u3067\u3042\u308b\u3002 S{displaystyle S} \u3092\u4efb\u610f\u306e\u30b9\u30ad\u30fc\u30e0\u3001 g\u22652{displaystyle ggeq 2} \u3092\u6574\u6570\u3068\u3059\u308b\u3002 S{displaystyle S} \u4e0a\u306e\u7a2e\u6570 g \u306e\u5b89\u5b9a\u66f2\u7dda\u3068\u306f\u3001\u56fa\u6709\u5e73\u5766\u5c04","datePublished":"2021-04-30","dateModified":"2022-09-14","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/4611d85173cd3b508e67077d4a1252c9c05abca2","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/4611d85173cd3b508e67077d4a1252c9c05abca2","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/1255","about":["Wiki"],"wordCount":4583,"articleBody":"\u5b89\u5b9a\u66f2\u7dda\uff08\u3042\u3093\u3066\u3044\u304d\u3087\u304f\u305b\u3093\u3001\u82f1: stable curve\uff09\u3068\u306f\u3001\u4ee3\u6570\u5e7e\u4f55\u5b66\u306e\u7528\u8a9e\u3067\u3001\u5e7e\u4f55\u5b66\u7684\u4e0d\u5909\u5f0f\u8ad6\u306e\u610f\u5473\u3067\u6f38\u8fd1\u7684\u306b\u5b89\u5b9a\u306a\u4ee3\u6570\u66f2\u7dda\u306e\u3053\u3068\u3067\u3042\u308b\u3002\u3053\u306e\u6761\u4ef6\u306f\u3001\u5b8c\u5099\u9023\u7d50\u66f2\u7dda\u3067\u3042\u3063\u3066\u3001\u305d\u306e\u7279\u7570\u70b9\u306f\u901a\u5e38\u4e8c\u91cd\u70b9\u306e\u307f\u3067\u3042\u308a\u3001\u304b\u3064\u81ea\u5df1\u540c\u5f62\u7fa4\uff08\u82f1\u8a9e\u7248\uff09\u304c\u6709\u9650\u7fa4\u3067\u3042\u308b\u3053\u3068\u3068\u540c\u5024\u3067\u3042\u308b\u3002\u81ea\u5df1\u540c\u5f62\u7fa4\u304c\u6709\u9650\u3067\u3042\u308b\u3068\u3044\u3046\u6761\u4ef6\u306f\u3001\u7b97\u8853\u7a2e\u6570\u304c1\u3067\u306f\u306a\u304f\u3001\u304b\u3064\u5168\u3066\u306e\u975e\u7279\u7570\u6709\u7406\u66f2\u7dda\u6210\u5206\u304c\u4ed6\u306e\u6210\u5206\u3068\u5c11\u306a\u304f\u3068\u30823\u70b9\u3067\u4ea4\u53c9\u3059\u308b\u3068\u3044\u3046\u6761\u4ef6\u306b\u7f6e\u304d\u63db\u3048\u3089\u308c\u308b[1]\u3002\u81ea\u5df1\u540c\u5f62\u7fa4\u306b\u6709\u9650\u7fa4\u3067\u306f\u306a\u304f\u7c21\u7d04\uff08reductive\uff09\u7fa4\u3092\u8a31\u3057\uff08\u3053\u308c\u306f\u9023\u7d50\u6210\u5206\u306b\u30c8\u30fc\u30e9\u30b9\u3092\u8a31\u3059\u3068\u3044\u3046\u6761\u4ef6\u3068\u540c\u5024\u3067\u3042\u308b\uff09\u3001\u307b\u304b\u306f\u540c\u69d8\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u3082\u306e\u3092\u534a\u5b89\u5b9a\u66f2\u7dda\uff08semi-stable curve\uff09\u3068\u3044\u3046[\u8981\u51fa\u5178]\u3002\u3042\u308b\u3044\u306f\u3001\u975e\u7279\u7570\u6709\u7406\u6210\u5206\u304c\u4ed6\u306e\u6210\u5206\u3068\u5c11\u306a\u304f\u3068\u30823\u70b9\u3067\u4ea4\u53c9\u3059\u308b\u3068\u3044\u3046\u6761\u4ef6\u3092\u3001\u5c11\u306a\u304f\u3068\u30822\u70b9\u3067\u4ea4\u53c9\u3059\u308b\u3068\u3044\u3046\u6761\u4ef6\u306b\u7f6e\u304d\u63db\u3048\u305f\u3082\u306e\u3067\u3042\u308b\u3002\u540c\u69d8\u306b\u3001\u6709\u9650\u500b\u306e\u6a19\u70b9\u4ed8\u304d\u66f2\u7dda\u304c\u5b89\u5b9a\u3068\u306f\u3001\u5b8c\u5099\u9023\u7d50\u3067\u3042\u3063\u3066\u7279\u7570\u70b9\u306f\u901a\u5e382\u91cd\u70b9\u306e\u307f\u3092\u6301\u3061\u81ea\u5df1\u540c\u5f62\u7fa4\u304c\u6709\u9650\u3067\u3042\u308b\u3053\u3068\u3092\u3044\u3046\u3002\u4f8b\u3048\u3070\u3001\u6955\u5186\u66f2\u7dda\uff08\u7a2e\u65701\u306e1\u6a19\u70b9\u4ed8\u304d\u975e\u7279\u7570\u66f2\u7dda\uff09\u306f\u5b89\u5b9a\u3067\u3042\u308b\u3002\u8907\u7d20\u6570\u4f53\u4e0a\u3067\u306f\u3001\u9023\u7d50\u306a\u66f2\u7dda\u304c\u5b89\u5b9a\u3067\u3042\u308b\u3053\u3068\u3068\u3001\u5168\u3066\u306e\u7279\u7570\u70b9\u3068\u6a19\u70b9\u3092\u9664\u304f\u3068\u5404\u6210\u5206\u306e\u666e\u904d\u88ab\u8986\u304c\u5358\u4f4d\u5186\u677f\u3068\u540c\u578b\u306b\u306a\u308b\u3053\u3068\u306f\u540c\u5024\u3067\u3042\u308b\u3002S{displaystyle S} \u3092\u4efb\u610f\u306e\u30b9\u30ad\u30fc\u30e0\u3001g\u22652{displaystyle ggeq 2} \u3092\u6574\u6570\u3068\u3059\u308b\u3002S{displaystyle S} \u4e0a\u306e\u7a2e\u6570 g \u306e\u5b89\u5b9a\u66f2\u7dda\u3068\u306f\u3001\u56fa\u6709\u5e73\u5766\u5c04 \u03c0:C\u2192S{displaystyle pi :Cto S} \u3067\u3042\u3063\u3066\u3001\u305d\u306e\u5e7e\u4f55\u5b66\u7684\u30d5\u30a1\u30a4\u30d0\u30fc Cs{displaystyle C_{s}} \u304c\u88ab\u7d04\u306a\u9023\u7d501\u6b21\u5143\u30b9\u30ad\u30fc\u30e0\u3067\u4ee5\u4e0b\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u3082\u306e\u3092\u8a00\u3046\u3002Cs{displaystyle C_{s}} \u306f\u901a\u5e382\u91cd\u70b9\u306e\u307f\u3092\u7279\u7570\u70b9\u3068\u3057\u3066\u6301\u3064\u5168\u3066\u306e\u6709\u7406\u66f2\u7dda\u6210\u5206\uff08rational component\uff09 E{displaystyle E} \u306f\u4ed6\u306e\u6210\u5206\u30682{displaystyle 2} \u70b9\u4ee5\u4e0a\u3067\u4ea4\u53c9\u3059\u308bdim\u2061H1(OCs)=g{displaystyle dim H^{1}({mathcal {O}}_{C_{s}})=g}\u3053\u308c\u3089\u306e\u30c6\u30af\u30cb\u30ab\u30eb\u306a\u6761\u4ef6\u306f\u3001\uff081\uff09\u6280\u8853\u7684\u306a\u8907\u96d1\u6027\u3092\u6e1b\u3089\u3057\u3001\u305d\u3057\u3066\u30d4\u30ab\u30fc\u30eb\u30fb\u30ec\u30d5\u30b7\u30a7\u30c3\u30c4\u7406\u8ad6\u306e\u9069\u7528\u3092\u53ef\u80fd\u306b\u3057\u3001\uff082\uff09\u3042\u3068\u3067\u69cb\u7bc9\u3059\u308b\u30e2\u30b8\u30e5\u30e9\u30a4\u30fb\u30b9\u30bf\u30c3\u30af\u304c\u7121\u9650\u5c0f\u81ea\u5df1\u540c\u578b\u3092\u6301\u305f\u306a\u3044\u3088\u3046\u306b\u66f2\u7dda\u3092\u786c\u5316\uff08rigidify\uff09\u3057\u3001\uff083\uff09\u5168\u3066\u306e\u30d5\u30a1\u30a4\u30d0\u30fc\u304c\u540c\u3058\u7b97\u8853\u7a2e\u6570\u3092\u3082\u3064\u3053\u3068\u3092\u4fdd\u8a3c\u3059\u308b\u305f\u3081\u306b\u5fc5\u8981\u3067\u3042\u308b\u3002\u306a\u304a\u3001\uff08\uff11\uff09\u306b\u95a2\u9023\u3057\u3066\u3001\u6955\u5186\u66f2\u9762\u306b\u751f\u3058\u5f97\u308b\u7279\u7570\u70b9\u306e\u7a2e\u985e\u306f\u5b8c\u5168\u306b\u5206\u985e\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u3067\u3042\u308b\u3053\u3068\u306b\u8a00\u53ca\u3057\u3066\u304a\u304f\u3002Table of Contents\u5b89\u5b9a\u66f2\u7dda\u306e\u4f8b[\u7de8\u96c6]\u5b89\u5b9a\u66f2\u7dda\u3067\u306f\u306a\u3044\u4f8b[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u5916\u90e8\u30ea\u30f3\u30af[\u7de8\u96c6]\u5b89\u5b9a\u66f2\u7dda\u306e\u4f8b[\u7de8\u96c6]\u5b89\u5b9a\u66f2\u7dda\u65cf\u306e\u53e4\u5178\u7684\u306a\u4f8b\u306f\u30ef\u30a4\u30a8\u30eb\u30b7\u30e5\u30c8\u30e9\u30b9\u66f2\u7dda\u65cfProj\u2061(Q[t][x,y,z](y2z\u2212x(x\u2212z)(x\u2212tz))\u2193Spec\u2061(Q[t]){displaystyle {begin{matrix}operatorname {Proj} left({frac {mathbb {Q} [t][x,y,z]}{(y^{2}z-x(x-z)(x-tz)}}right)downarrow operatorname {Spec} (mathbb {Q} [t])end{matrix}}}  \u3067\u3042\u308b\u3002\u3053\u306e\u66f2\u7dda\u65cf\u306f\u30010,1{displaystyle 0,1} \u3092\u9664\u304f\u5168\u3066\u306e\u70b9\u306e\u4e0a\u3067\u305d\u306e\u30d5\u30a1\u30a4\u30d0\u30fc\u306f\u6ed1\u3089\u304b\u3067\u3001\u9000\u5316\u3059\u308b\u70b9\u3067\u3082\u305d\u306e\u30d5\u30a1\u30a4\u30d0\u30fc\u306f2\u91cd\u70b9\u3092\u7279\u7570\u70b9\u3068\u3057\u3066\u6301\u3064\u306e\u307f\u3067\u3042\u308b\u3002\u3053\u306e\u4f8b\u306f\u3001\u6709\u9650\u500b\u306e\u70b9\u306e\u307f\u3067\u9000\u5316\u3059\u308b\u6ed1\u3089\u304b\u306a\u8d85\u6955\u5186\u66f2\u7dda\u306e 1 \u30d1\u30e9\u30e1\u30fc\u30bf\u65cf\u306b\u4e00\u822c\u5316\u3067\u304d\u308b\u3002\u5b89\u5b9a\u66f2\u7dda\u3067\u306f\u306a\u3044\u4f8b[\u7de8\u96c6]\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u6570\u304c1\u3088\u308a\u3082\u5927\u304d\u306a\u4e00\u822c\u306e\u5834\u5408\u3067\u306f\u30012\u91cd\u70b9\u3088\u308a\u3082\u60aa\u3044\u7279\u7570\u70b9\u3092\u542b\u3080\u66f2\u7dda\u3092\u53d6\u308a\u9664\u304f\u306e\u306b\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3042\u308b\u3002\u4f8b\u3068\u3057\u3066\u3001\u6b21\u306e\u591a\u9805\u5f0f  y2=x(x\u2212s)(x\u2212t)(x\u22121)(x\u22122){displaystyle y^{2}=x(x-s)(x-t)(x-1)(x-2)}\u3092\u8003\u3048\u308b\u3002\u3053\u308c\u304c\u5b9a\u7fa9\u3059\u308b As,t2{displaystyle mathbb {A} _{s,t}^{2}} \u4e0a\u306e\u65cf\u306f\u3001\u5bfe\u89d2\u7dda s=t{displaystyle s=t} \u4e0a\u306b2\u91cd\u70b9\u3067\u306f\u306a\u3044\u7279\u7570\u70b9\u304c\u3042\u308b\u3002\u3082\u3046\u4e00\u3064\u306e\u5b89\u5b9a\u66f2\u7dda\u3067\u306f\u306a\u3044\u4f8b\u306f\u3001\u6b21\u306e\u591a\u9805\u5f0f  x3\u2212y2+t{displaystyle x^{3}-y^{2}+t}\u3067\u4e0e\u3048\u3089\u308c\u308b At1{displaystyle mathbb {A} _{t}^{1}} \u4e0a\u306e\u65cf\u3067\u3042\u308b\u3002\u3053\u308c\u306f\u5c16\u70b9\u30921\u3064\u6301\u3064\u6709\u7406\u66f2\u7dda\u306b\u9000\u5316\u3059\u308b\u6955\u5186\u66f2\u7dda\u306e\u65cf\u3067\u3042\u308b\u3002\u5b89\u5b9a\u66f2\u7dda\u306e\u6700\u3082\u91cd\u8981\u306a\u6027\u8cea\u306e\u4e00\u3064\u306f\u3001\u5c40\u6240\u7684\u306b\u5b8c\u5168\u4ea4\u53c9\u3067\u3042\u308b\u3053\u3068\u3067\u3042\u308b\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u6a19\u6e96\u7684\u306a\u30bb\u30fc\u30eb\u53cc\u5bfe\u6027\u306e\u7406\u8ad6\u3092\u9069\u7528\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u7279\u306b\u3001\u4efb\u610f\u306e\u5b89\u5b9a\u66f2\u7dda\u306b\u5bfe\u3057\u3066 \u03c9C\/S\u22973{displaystyle omega _{C\/S}^{otimes 3}} \u306f\u76f8\u5bfe\u7684\u306b\u975e\u5e38\u306b\u8c4a\u5bcc\u306a\u5c64\uff08relatively very-ample sheaf\uff09\u3067\u3042\u308b\u3053\u3068\u304c\u793a\u3055\u308c\u308b\u3002\u3053\u308c\u3092\u4f7f\u3063\u3066\u5b89\u5b9a\u66f2\u7dda\u3092 PS5g\u22126{displaystyle mathbb {P} _{S}^{5g-6}} \u3078\u57cb\u3081\u8fbc\u3080\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u5c04\u5f71\u7a7a\u9593\u306b\u57cb\u3081\u8fbc\u307e\u308c\u305f\u7a2e\u6570 g{displaystyle g} \u306e\u66f2\u7dda\u306e\u30e2\u30b8\u30e5\u30e9\u30a4\u30fb\u30b9\u30ad\u30fc\u30e0\u306f\u3001\u30d2\u30eb\u30d9\u30eb\u30c8\u30b9\u30ad\u30fc\u30e0\u306e\u6a19\u6e96\u7684\u306a\u7406\u8ad6\u3092\u7528\u3044\u3066\u69cb\u7bc9\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u305d\u306e\u3068\u304d\u306e\u30d2\u30eb\u30d9\u30eb\u30c8\u591a\u9805\u5f0f\u306fPg(n)=(6n\u22121)(g\u22121){displaystyle P_{g}(n)=(6n-1)(g-1)}\u3067\u4e0e\u3048\u3089\u308c\u308b\u3002\u3053\u306e\u30d2\u30eb\u30d9\u30eb\u30c8\u30b9\u30ad\u30fc\u30e0\u306b\u306f\u3001\u5b89\u5b9a\u66f2\u7dda\u306b\u5bfe\u5fdc\u3059\u308b\u70b9\u304b\u3089\u306a\u308b\u90e8\u5206\u7a7a\u9593Hg\u2282HilbPZ5g\u22126Pg{displaystyle H_{g}subset {textbf {Hilb}}_{mathbb {P} _{mathbb {Z} }^{5g-6}}^{P_{g}}}\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u3002\u3053\u306e\u7a7a\u9593\u306f\u3001\u95a2\u624bMg(S)\u2245{stable curves\u00a0\u03c0:C\u2192S\u00a0with an iso\u00a0P(\u03c0\u2217(\u03c9C\/S\u22973))\u2245P5g\u22126\u00d7S}\/\u223c\u2245Hom\u2061(S,Hg){displaystyle {mathcal {M}}_{g}(S)cong left.left{{begin{matrix}&{text{stable curves }}pi :Cto S&{text{ with an iso }}&mathbb {P} (pi _{*}(omega _{C\/S}^{otimes 3}))cong mathbb {P} ^{5g-6}times Send{matrix}}right}{Bigg \/}{sim }right.cong operatorname {Hom} (S,H_{g})}\u306e\u8868\u73fe\u306b\u306a\u3063\u3066\u3044\u308b\u3002\u3053\u3053\u3067\u3001\u223c{displaystyle sim } \u306f\u5b89\u5b9a\u66f2\u7dda\u306e\u540c\u578b\u5199\u50cf\u306b\u3088\u308b\u540c\u5024\u95a2\u4fc2\u3067\u3042\u308b\u3002\u3053\u306e\u7a7a\u9593\u304b\u3089\u3001\u5c04\u5f71\u7a7a\u9593\u3078\u306e\u57cb\u3081\u8fbc\u307f\u3092\u5916\u3057\u305f\u66f2\u7dda\u305d\u306e\u3082\u306e\u306e\u30e2\u30b8\u30e5\u30e9\u30a4\u7a7a\u9593\u3092\u5f97\u308b\u305f\u3081\u306b\u306f\u3001\u5c04\u5f71\u7a7a\u9593\u3078\u306e\u57cb\u3081\u8fbc\u307f\u306f\u5c04\u5f71\u7a7a\u9593\u306e\u540c\u578b\u5199\u50cf\u306b\u5bfe\u5fdc\u3055\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u306e\u3067\u3001PGL(5g\u22126){displaystyle PGL(5g-6)} \u306b\u3088\u308b\u5546\u3092\u53d6\u308c\u3070\u3088\u3044\u3002\u3053\u3046\u3057\u3066\u30e2\u30b8\u30e5\u30e9\u30a4\u30fb\u30b9\u30bf\u30c3\u30afMg:=[H_g\/PGL_(5g\u22126)]{displaystyle {mathcal {M}}_{g}:=[{underline {H}}_{g}\/{underline {PGL}}(5g-6)]}\u304c\u5f97\u3089\u308c\u308b\u3002\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]Artin, M.; Winters, G. (1971-11-01). “Degenerate fibres and stable reduction of curves“. Topology. 10 (4): 373\u2013383. doi:10.1016\/0040-9383(71)90028-0. ISSN\u00a00040-9383.Deligne, Pierre; Mumford, David (1969), \u201cThe irreducibility of the space of curves of given genus\u201d, Publications Math\u00e9matiques de l’IH\u00c9S 36 (36):  75\u2013109, doi:10.1007\/BF02684599, MR0262240, http:\/\/www.numdam.org\/item?id=PMIHES_1969__36__75_0\u00a0Gieseker, D. (1982), Lectures on moduli of curves, Tata Institute of Fundamental Research Lectures on Mathematics and Physics, 69, Published for the Tata Institute of Fundamental Research, Bombay, ISBN\u00a0978-3-540-11953-1, MR691308, http:\/\/www.math.tifr.res.in\/~publ\/ln\/tifr69.pdf\u00a0Harris, Joe; Morrison, Ian (1998), Moduli of curves, Graduate Texts in Mathematics, 187, Berlin, New York: Springer-Verlag, ISBN\u00a0978-0-387-98429-2, MR1631825\u00a0\u5916\u90e8\u30ea\u30f3\u30af[\u7de8\u96c6]Casalaina-Martin, Sebastian (2021). “A tour of stable reduction with applications” (\u82f1\u8a9e). arXiv:1207.1048 [math]\u3002"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki6\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/1255#breadcrumbitem","name":"\u5b89\u5b9a\u66f2\u7dda – Wikipedia"}}]}]