Quadratic equations of tangent varieties via four-way tensors of linear forms
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916985537822720 |
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| author | Choe, Junho |
| author_facet | Choe, Junho |
| contents | In the present paper we construct quadratic equations and linear syzygies for tangent varieties using 4-way tensors of linear forms and generalize this method to higher secant varieties of higher osculating varieties. Such equations extend the classical determinantal ones of higher secant varieties and span all the equations of the same degree for smooth projective curves completely embedded by sufficiently positive line bundles, proving a variant of the Eisenbud-Koh-Stillman conjecture on determinantal equations. On the other hand, our syzygies are compatible with the Green-Lazarsfeld classes and generate the corresponding Koszul cohomology groups for Segre varieties with a prescribed number of factors. To obtain these results we describe the equations of minimal possible degrees and reinterpret the Green-Lazarsfeld classes from the perspective of representation theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01908 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quadratic equations of tangent varieties via four-way tensors of linear forms Choe, Junho Algebraic Geometry Commutative Algebra 14N05, 13D02 In the present paper we construct quadratic equations and linear syzygies for tangent varieties using 4-way tensors of linear forms and generalize this method to higher secant varieties of higher osculating varieties. Such equations extend the classical determinantal ones of higher secant varieties and span all the equations of the same degree for smooth projective curves completely embedded by sufficiently positive line bundles, proving a variant of the Eisenbud-Koh-Stillman conjecture on determinantal equations. On the other hand, our syzygies are compatible with the Green-Lazarsfeld classes and generate the corresponding Koszul cohomology groups for Segre varieties with a prescribed number of factors. To obtain these results we describe the equations of minimal possible degrees and reinterpret the Green-Lazarsfeld classes from the perspective of representation theory. |
| title | Quadratic equations of tangent varieties via four-way tensors of linear forms |
| topic | Algebraic Geometry Commutative Algebra 14N05, 13D02 |
| url | https://arxiv.org/abs/2510.01908 |