{"id":1001,"date":"2025-10-01T10:58:44","date_gmt":"2025-10-01T08:58:44","guid":{"rendered":"http:\/\/blog.mathyuan.com\/?p=1001"},"modified":"2026-03-04T22:28:06","modified_gmt":"2026-03-04T21:28:06","slug":"%e3%80%8c%e5%9f%ba%e7%a1%80%e4%bb%a3%e6%95%b0%e5%87%a0%e4%bd%95%e3%80%8d%e8%8d%9f%e8%90%83","status":"publish","type":"post","link":"https:\/\/blog.mathyuan.com\/?p=1001","title":{"rendered":"\u300c\u57fa\u7840\u4ee3\u6570\u51e0\u4f55\u300d\u835f\u8403"},"content":{"rendered":"

\u6709\u4e00\u4e9b\u300c\u57fa\u7840\u4ee3\u6570\u51e0\u4f55\u300d\u8bfe\u7a0b\u4e2d\u7b80\u77ed\u6709\u8da3\u7684\u4e60\u9898\u3001\u7ed3\u8bba\uff0c\u5199\u5728\u4fbf\u6761\u4e0a\u65b9\u4fbf\u8bb0\u5fc6\u3002\u73b0\u5728\u6574\u7406\u4e0b\u6765\u653e\u5728\u7f51\u4e0a\uff0c\u5c31\u53ef\u4ee5\u6e05\u7406\u6389\u7eb8\u8d28\u4fbf\u6761\u4e86\u3002<\/p>\n

1. \u82e5\u590d\u4eff\u5c04\u7c07\u7684\u7ef4\u6570\u5927\u4e8e\u6216\u7b49\u4e8e1\uff0c\u5219\u5176\u4f5c\u4e3a$\\mathbb{C}^n$\u5b50\u7a7a\u95f4\u65f6\u8d4b\u4e88classical topology\u65f6\uff0c\u4e00\u5b9a\u4e0d\u662f\u7d27\u81f4\u7684\uff1b<\/p>\n

2. \u5b58\u5728projective varieties $X$\u548c$Y$\uff0c\u4f7f\u5f97$X\\cong Y$\uff0c\u4f46$S(X)\\not\\cong S(Y)$\uff0c\u8fd9\u5c31\u8bf4\u660eprojective variety\u7684\u9f50\u6b21\u591a\u9879\u5f0f\u73af\u4e0d\u662fprojective variety\u7684\u4e0d\u53d8\u91cf\uff1b<\/p>\n

3. \u82e5$X$\u662f\u9884\u7c07\uff0c$Y$\u662f\u4eff\u5c04\u7c07\uff0c\u5219\u5b58\u5728\u4e00\u4e00\u5bf9\u5e94
\n$$
\n\\mathrm{Mor}(X,Y)\\leftrightarrow\\mathrm{Hom}(\\mathcal{O}_Y(Y),\\mathcal{O}_X(X))
\n$$
\n\u4f46\u5728\u6539\u53d8\u6761\u4ef6\u65f6\u6709\u53ef\u80fd\u4e0d\u6210\u7acb\uff0c\u5373\u4e0d\u53ef\u4ee5\u53ea\u8981\u6c42$X$\u662f\u4eff\u5c04\u7c07\u800c$Y$\u662f\u9884\u7c07\uff0c\u4e00\u4e2a\u53cd\u4f8b\u662f$X=\\mathbb{A}^1$\u548c$Y=\\mathbb{P}^1$\uff1b<\/p>\n

4.<\/p>\n","protected":false},"excerpt":{"rendered":"

\u6536\u96c6\u7684\u4e00\u4e9b\u7b80\u77ed\u8bfe\u7a0b\u4e60\u9898\uff0c\u6301\u7eed\u66f4\u65b0\u2026\u2026 \u7ee7\u7eed\u9605\u8bfb \u300c\u57fa\u7840\u4ee3\u6570\u51e0\u4f55\u300d\u835f\u8403<\/span>→<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9],"tags":[11,8],"class_list":["post-1001","post","type-post","status-publish","format-standard","hentry","category-notes","tag-11","tag-8"],"_links":{"self":[{"href":"https:\/\/blog.mathyuan.com\/index.php?rest_route=\/wp\/v2\/posts\/1001","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.mathyuan.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.mathyuan.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.mathyuan.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.mathyuan.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1001"}],"version-history":[{"count":6,"href":"https:\/\/blog.mathyuan.com\/index.php?rest_route=\/wp\/v2\/posts\/1001\/revisions"}],"predecessor-version":[{"id":1073,"href":"https:\/\/blog.mathyuan.com\/index.php?rest_route=\/wp\/v2\/posts\/1001\/revisions\/1073"}],"wp:attachment":[{"href":"https:\/\/blog.mathyuan.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1001"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.mathyuan.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1001"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.mathyuan.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1001"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}