Secant planes of a general curve via degenerations
Algebraic Geometry
2020-06-30 v3 Combinatorics
Abstract
We study linear series on a general curve of genus g, whose images are exceptional with respect to their secant planes. Each such exceptional secant plane is algebraically encoded by an included linear series, whose number of base points computes the incidence degree of the corresponding secant plane. With enumerative applications in mind, we construct a moduli scheme of inclusions of limit linear series with base points over families of nodal curves of compact type, which we then use to compute combinatorial formulas for the number of secant-exceptional linear series when the spaces of linear series and of inclusions are finite.
Cite
@article{arxiv.1901.06430,
title = {Secant planes of a general curve via degenerations},
author = {Ethan Cotterill and Xiang He and Naizhen Zhang},
journal= {arXiv preprint arXiv:1901.06430},
year = {2020}
}
Comments
37 pages, final version, to appear in Geometriae Dedicata