Degree of the 3-secant variety
Algebraic Geometry
2025-01-23 v4
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.
Keywords
Cite
@article{arxiv.2302.00913,
title = {Degree of the 3-secant variety},
author = {Doyoung Choi},
journal= {arXiv preprint arXiv:2302.00913},
year = {2025}
}
Comments
15 pages