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arXiv · 2302.00913

Degree of the 3-secant variety

Doyoung Choi
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Abstract

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.

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Doyoung Choi. 2023-02-02. Degree of the 3-secant variety. https://arxiv.org/abs/2302.00913

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