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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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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Additional Information
  • Melody Chan
  • Affiliation: Department of Mathematics, Brown University, Box 1917, Providence, Rhode Island 02912
  • MR Author ID: 791839
  • Email: melody_chan@brown.edu
  • Nathan Pflueger
  • Affiliation: Department of Mathematics and Statistics, Amherst College, Amherst, Massachusetts 01002
  • MR Author ID: 950261
  • ORCID: 0000-0002-9579-9630
  • Email: npflueger@amherst.edu
  • Received by editor(s): October 17, 2019
  • Received by editor(s) in revised form: February 13, 2020
  • Published electronically: November 3, 2020
  • Additional Notes: The first author was supported by an NSA Young Investigators Grant, NSF DMS-1701924, and a Sloan Research Fellowship.
  • © Copyright 2020 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 374 (2021), 1513-1533
  • MSC (2010): Primary 14H51, 14M15, 05E05
  • DOI: https://doi.org/10.1090/tran/8164
  • MathSciNet review: 4216716