Some local and global properties of secant varieties of nonsingular projective curves

Lawrence Ein; Wenbo Niu; Jinhyung Park

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arXiv · 2604.26054

Some local and global properties of secant varieties of nonsingular projective curves

Lawrence Ein·Wenbo Niu·Jinhyung Park

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Abstract

The main goal of this paper is to study some local and global properties of secant varieties of algebraic curves. These results complement our previous work [8] by addressing issues given therein and providing solutions to problems raised subsequently. Specifically, we show a description of tangent cones of secant varieties of curves, and compute the cohomology groups of secant sheaves on symmetric products of curves, which answers a question posed in [8] and leads to a recursive formula for Hilbert polynomials of secant varieties of curves. In the appendix, we present a cohomological approach to arithmetical Cohen--Macaulayness of secant varieties of curves, completing the proof in [8].

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Lawrence Ein, Wenbo Niu, Jinhyung Park. 2026-04-28. Some local and global properties of secant varieties of nonsingular projective curves. https://arxiv.org/abs/2604.26054

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