Linear series on general curves with prescribed incidence conditions
Gavril Farkas, Carl Lian

TL;DR
This paper computes the number of linear series with prescribed incidence conditions on general curves, using degeneration and Schubert calculus, providing complete formulas for large degrees and special cases.
Contribution
It offers new formulas and proofs for counting linear series with incidence conditions on general curves, extending previous results.
Findings
Complete formulas for linear series counts when degree is large
Explicit counts for cases where r=1 or n=r+2
Generalization of recent results by Tevelev and Cela-Pandharipande-Schmitt
Abstract
Using degeneration and Schubert calculus, we consider the problem of computing the number of linear series of given degree and dimension on a general curve of genus satisfying prescribed incidence conditions at points. We determine these numbers completely for linear series of arbitrary dimension when is sufficiently large, and for all when either or . Our formulas generalize and give new proofs of recent results of Tevelev and of Cela-Pandharipande-Schmitt.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Meromorphic and Entire Functions · Advanced Combinatorial Mathematics
