Work

Euler characteristics of Brill-Noether varieties

Year: 2020

Type: article

Abstract: We prove an enumerative formula for the algebraic Euler characteristic of Brill-Noether varieties, parametrizing degree d d and rank r r linear series on a general genus g 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 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.

Source: Transactions of the American Mathematical Society

DOI: 10.1090/tran/8164

Authors: Melody Chan, Nathan Pflueger

Institutions: Brown University, Amherst College

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Alfred P. Sloan Foundation, National Security Agency

Awards: G1603829500, G3841877688, G3912582971, Algebraic and Tropical Moduli Spaces and Brill-Noether Theory, G5085127431