Euler characteristics of Brill-Noether varieties

Chan, Melody; Pflueger, Nathan

doi:10.1090/tran/8164

Euler characteristics of Brill-Noether varieties
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by Melody Chan and Nathan Pflueger PDF

Trans. Amer. Math. Soc. 374 (2021), 1513-1533 Request permission

Abstract:

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 Murray-Osserman; the count of set-valued tableaux is an explicit enumeration of strata of this degeneration.

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