The Gieseker-Petri theorem and imposed ramification
Algebraic Geometry
2020-10-29 v2
Abstract
We prove a smoothness result for spaces of linear series with prescribed ramification on twice-marked elliptic curves. In characteristic 0, we then apply the Eisenbud-Harris theory of limit linear series to deduce a new proof of the Gieseker-Petri theorem, along with a generalization to spaces of linear series with prescribed ramification at up to two points. Our main calculation involves the intersection of two Schubert cycles in a Grassmannian associated to almost-transverse flags.
Cite
@article{arxiv.1804.00178,
title = {The Gieseker-Petri theorem and imposed ramification},
author = {Melody Chan and Brian Osserman and Nathan Pflueger},
journal= {arXiv preprint arXiv:1804.00178},
year = {2020}
}
Comments
17 pages, revised version published in Bull. London Math. Soc