{"title":"关于三次四重的一些不变量。","authors":"Frank Gounelas, Alexis Kouvidakis","doi":"10.1007/s40879-023-00651-y","DOIUrl":null,"url":null,"abstract":"<p><p>For a general cubic fourfold <math><mrow><mi>X</mi><mo>⊂</mo><msup><mrow><mi>P</mi></mrow><mn>5</mn></msup></mrow></math> with Fano variety <i>F</i>, we compute the Hodge numbers of the locus <math><mrow><mi>S</mi><mo>⊂</mo><mi>F</mi></mrow></math> of lines of second type and the class of the locus <math><mrow><mi>V</mi><mo>⊂</mo><mi>F</mi></mrow></math> of triple lines, using the description of the latter in terms of flag varieties. We also give an upper bound of 6 for the degree of irrationality of the Fano scheme of lines of any smooth cubic hypersurface.</p>","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":"9 3","pages":"58"},"PeriodicalIF":0.5000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10335978/pdf/","citationCount":"3","resultStr":"{\"title\":\"On some invariants of cubic fourfolds.\",\"authors\":\"Frank Gounelas, Alexis Kouvidakis\",\"doi\":\"10.1007/s40879-023-00651-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>For a general cubic fourfold <math><mrow><mi>X</mi><mo>⊂</mo><msup><mrow><mi>P</mi></mrow><mn>5</mn></msup></mrow></math> with Fano variety <i>F</i>, we compute the Hodge numbers of the locus <math><mrow><mi>S</mi><mo>⊂</mo><mi>F</mi></mrow></math> of lines of second type and the class of the locus <math><mrow><mi>V</mi><mo>⊂</mo><mi>F</mi></mrow></math> of triple lines, using the description of the latter in terms of flag varieties. We also give an upper bound of 6 for the degree of irrationality of the Fano scheme of lines of any smooth cubic hypersurface.</p>\",\"PeriodicalId\":44725,\"journal\":{\"name\":\"European Journal of Mathematics\",\"volume\":\"9 3\",\"pages\":\"58\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10335978/pdf/\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"European Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s40879-023-00651-y\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2023/7/11 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s40879-023-00651-y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2023/7/11 0:00:00","PubModel":"Epub","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
For a general cubic fourfold with Fano variety F, we compute the Hodge numbers of the locus of lines of second type and the class of the locus of triple lines, using the description of the latter in terms of flag varieties. We also give an upper bound of 6 for the degree of irrationality of the Fano scheme of lines of any smooth cubic hypersurface.
期刊介绍：
The European Journal of Mathematics (EJM) is an international journal that publishes research papers in all fields of mathematics. It also publishes research-survey papers intended to provide nonspecialists with insight into topics of current research in different areas of mathematics. The journal invites authors from all over the world. All contributions are required to meet high standards of quality and originality. EJM has an international editorial board. Coverage in EJM will include: - Algebra - Complex Analysis - Differential Equations - Discrete Mathematics - Functional Analysis - Geometry and Topology - Mathematical Logic and Foundations - Number Theory - Numerical Analysis and Optimization - Probability and Statistics - Real Analysis.
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