Linear series on general curves with prescribed incidence conditions

Gavril Farkas; Carl Lian

Linear series on general curves with prescribed incidence conditions

Algebraic Geometry 2022-02-24 v2 Combinatorics

Authors: Gavril Farkas , Carl Lian

Abstract

Using degeneration and Schubert calculus, we consider the problem of computing the number of linear series of given degree $d$ and dimension $r$ on a general curve of genus $g$ satisfying prescribed incidence conditions at $n$ points. We determine these numbers completely for linear series of arbitrary dimension when $d$ is sufficiently large, and for all $d$ when either $r=1$ or $n=r+2$ . Our formulas generalize and give new proofs of recent results of Tevelev and of Cela-Pandharipande-Schmitt.

Keywords

linear series general curves incidence conditions Schubert calculus degeneration genus g curves

Cite

@article{arxiv.2105.09340,
  title  = {Linear series on general curves with prescribed incidence conditions},
  author = {Gavril Farkas and Carl Lian},
  journal= {arXiv preprint arXiv:2105.09340},
  year   = {2022}
}

Comments

version 2, various corrections (including error in section 4), plus references to later work. To appear in J. Inst. Math. Jussieu

Linear series on general curves with prescribed incidence conditions

Abstract

Keywords

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