# Euler characteristics of Brill-Noether varieties

@article{Chan2017EulerCO,
title={Euler characteristics of Brill-Noether varieties},
author={Melody Chan and Nathan Pflueger},
journal={arXiv: Algebraic Geometry},
year={2017}
}
• Published 30 August 2017
• Mathematics
• arXiv: Algebraic Geometry
We prove an enumerative formula for the algebraic Euler characteristic of Brill-Noether varieties, parametrizing degree d and rank r linear series on a general genus g curve, with ramification profiles specified at up to two general points. Up to sign, this Euler characteristic is the number of standard set-valued tableaux of a certain skew shape with g labels. We use a flat degeneration via the Eisenbud-Harris theory of limit-linear series, relying on moduli-theoretic advances of Osserman and…

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