Linear series on general curves with prescribed incidence conditions

Gavril Farkas, Carl Lian

Published 2021-05-19Version 1

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.