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On hyperquadrics containing projective varieties
| Content Provider | Scilit |
|---|---|
| Author | Park, Euisung |
| Copyright Year | 2020 |
| Abstract | Classical Castelnuovo Lemma shows that the number of linearly independent quadratic equations of a nondegenerate irreducible projective variety of codimension c is at most {{{c+1}\choose{2}}} and the equality is attained if and only if the variety is of minimal degree. Also G. Fano’s generalization of Castelnuovo Lemma implies that the next case occurs if and only if the variety is a del Pezzo variety. Recently, these results are extended to the next case in [E. Park, On hypersurfaces containing projective varieties, Forum Math. 27 2015, 2, 843–875]. This paper is intended to complete the classification of varieties satisfying at least {{{c+1}\choose{2}}-3} linearly independent quadratic equations. Also we investigate the zero set of those quadratic equations and apply our results to projective varieties of degree {\geq 2c+1} . |
| Related Links | https://www.degruyter.com/downloadpdf/journals/form/ahead-of-print/article-10.1515-forum-2019-0275/article-10.1515-forum-2019-0275.pdf |
| Ending Page | 1209 |
| Page Count | 11 |
| Starting Page | 1199 |
| ISSN | 09337741 |
| e-ISSN | 14355337 |
| DOI | 10.1515/forum-2019-0275 |
| Journal | Forum Mathematicum |
| Issue Number | 5 |
| Volume Number | 32 |
| Language | English |
| Publisher | Walter de Gruyter GmbH |
| Publisher Date | 2020-06-11 |
| Access Restriction | Open |
| Subject Keyword | Forum Mathematicum Logic Quadratic Equations Projective Varieties of Low Degree Castelnuovo Theory 14n05 14n25 Journal: Forum Mathematicum, Vol- 32 |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
