Degree of the 3-secant variety
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929683569836032 |
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| author | Choi, Doyoung |
| author_facet | Choi, Doyoung |
| contents | In this paper, we present a formula for the degree of the 3-secant variety of a nonsingular projective variety embedded by a 5-very ample line bundle. The formula is provided in terms of Segre classes of the tangent bundle of a given variety. We use the generalized version of double point formula to reduce the calculation into the case of the 2-secant variety. Due to the singularity of the 2-secant variety, we use secant bundle as a nonsingular birational model and compute multiplications of desired algebraic cycles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_00913 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Degree of the 3-secant variety Choi, Doyoung Algebraic Geometry Primary14N07secondary14C2514N10 In this paper, we present a formula for the degree of the 3-secant variety of a nonsingular projective variety embedded by a 5-very ample line bundle. The formula is provided in terms of Segre classes of the tangent bundle of a given variety. We use the generalized version of double point formula to reduce the calculation into the case of the 2-secant variety. Due to the singularity of the 2-secant variety, we use secant bundle as a nonsingular birational model and compute multiplications of desired algebraic cycles. |
| title | Degree of the 3-secant variety |
| topic | Algebraic Geometry Primary14N07secondary14C2514N10 |
| url | https://arxiv.org/abs/2302.00913 |