Hilbert polynomials of the first and second secant varieties
math.AG2026-05v1license
Abstract
In this paper, we give a description of the cohomology groups of the symmetric powers of the tautological bundle associated with a sufficiently positive line bundle on the Hilbert scheme of 2 or 3 points on a smooth projective complex variety. The dimensions of these cohomology groups are expressed in terms of the Hilbert polynomials of the first and second secant varieties of the embedding given by the sufficiently positive line bundle. We also compute these Hilbert polynomials completely.
Cite
@article{arxiv.2605.29418,
title = {Hilbert polynomials of the first and second secant varieties},
author = {Doyoung Choi and Jinhyung Park},
journal= {arXiv preprint arXiv:2605.29418},
year = {2026}
}