{"title":"特级加权超曲面的合理性","authors":"Michael Chitayat","doi":"10.1016/j.jalgebra.2024.10.032","DOIUrl":null,"url":null,"abstract":"<div><div>Let <span><math><mi>X</mi><mo>⊂</mo><mi>P</mi><mo>(</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>)</mo></math></span> be a quasismooth well-formed weighted projective hypersurface and let <span><math><mi>L</mi><mo>=</mo><mi>lcm</mi><mo>(</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>)</mo></math></span>. We characterize when <em>X</em> is rational under the assumption that <em>L</em> divides <span><math><mi>deg</mi><mo></mo><mo>(</mo><mi>X</mi><mo>)</mo></math></span>. Furthermore, we give a new family of normal rational weighted projective hypersurfaces with ample canonical divisor, valid in all dimensions, adding to the list of examples discovered by Kollár. Finally, we determine precisely which affine Pham-Brieskorn threefolds are rational, answering a question of Rajendra V. Gurjar.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"665 ","pages":"Pages 7-29"},"PeriodicalIF":0.8000,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Rationality of weighted hypersurfaces of special degree\",\"authors\":\"Michael Chitayat\",\"doi\":\"10.1016/j.jalgebra.2024.10.032\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Let <span><math><mi>X</mi><mo>⊂</mo><mi>P</mi><mo>(</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>)</mo></math></span> be a quasismooth well-formed weighted projective hypersurface and let <span><math><mi>L</mi><mo>=</mo><mi>lcm</mi><mo>(</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>)</mo></math></span>. We characterize when <em>X</em> is rational under the assumption that <em>L</em> divides <span><math><mi>deg</mi><mo></mo><mo>(</mo><mi>X</mi><mo>)</mo></math></span>. Furthermore, we give a new family of normal rational weighted projective hypersurfaces with ample canonical divisor, valid in all dimensions, adding to the list of examples discovered by Kollár. Finally, we determine precisely which affine Pham-Brieskorn threefolds are rational, answering a question of Rajendra V. Gurjar.</div></div>\",\"PeriodicalId\":14888,\"journal\":{\"name\":\"Journal of Algebra\",\"volume\":\"665 \",\"pages\":\"Pages 7-29\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-11-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021869324005921\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021869324005921","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
设 X⊂P(w0,w1,w2,w3)是一个准光滑的完形加权投影超曲面，设 L=lcm(w0,w1,w2,w3).假设 L 平分 deg(X)，我们将描述当 X 为有理时的特征。此外，我们还给出了在所有维度上都有效的、具有充裕典范除数的正常有理加权投影超曲面的一个新族，为 Kollár 发现的例子列表增添了新的内容。最后，我们精确地确定了哪些仿射 Pham-Brieskorn 三折是有理的，回答了 Rajendra V. Gurjar 的一个问题。
Rationality of weighted hypersurfaces of special degree
Let be a quasismooth well-formed weighted projective hypersurface and let . We characterize when X is rational under the assumption that L divides . Furthermore, we give a new family of normal rational weighted projective hypersurfaces with ample canonical divisor, valid in all dimensions, adding to the list of examples discovered by Kollár. Finally, we determine precisely which affine Pham-Brieskorn threefolds are rational, answering a question of Rajendra V. Gurjar.
期刊介绍：
The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
