TY - JOUR
T1 - LINEAR SERIES ON GENERAL CURVES WITH PRESCRIBED INCIDENCE CONDITIONS
AU - Farkas, Gavril
AU - Lian, Carl
N1 - Publisher Copyright:
© The Author(s), 2022. Published by Cambridge University Press.
PY - 2023/11/6
Y1 - 2023/11/6
N2 - 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 generalise and give new proofs of recent results of Tevelev and of Cela, Pandharipande and Schmitt.
AB - 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 generalise and give new proofs of recent results of Tevelev and of Cela, Pandharipande and Schmitt.
KW - 14H10
UR - https://www.scopus.com/pages/publications/85175636103
U2 - 10.1017/S1474748022000251
DO - 10.1017/S1474748022000251
M3 - Article
AN - SCOPUS:85175636103
SN - 1474-7480
VL - 22
SP - 2857
EP - 2877
JO - Journal of the Institute of Mathematics of Jussieu
JF - Journal of the Institute of Mathematics of Jussieu
IS - 6
ER -