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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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A pointed Prym–Petri Theorem
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by Nicola Tarasca PDF
Trans. Amer. Math. Soc. 376 (2023), 2641-2656 Request permission


We construct pointed Prym–Brill–Noether varieties parametrizing line bundles assigned to an irreducible étale double covering of a curve with a prescribed minimal vanishing at a fixed point. We realize them as degeneracy loci in type D and deduce their classes in case of expected dimension. Thus, we determine a pointed Prym–Petri map and prove a pointed version of the Prym–Petri theorem implying that the expected dimension holds in the general case. These results build on work of Welters [Ann. Sci. Ëcole Norm. Sup. (4) 18 (1985), pp. 671–683] and De Concini–Pragacz [Math. Ann. 302 (1995), pp. 687–697] on the unpointed case. Finally, we show that Prym varieties are Prym–Tyurin varieties for Prym–Brill–Noether curves of exponent enumerating standard shifted tableaux times a factor of $2$, extending to the Prym setting work of Ortega [Math. Ann. 356 (2013), pp. 809–817].
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Additional Information
  • Nicola Tarasca
  • Affiliation: Department of Mathematics & Applied Mathematics, Virginia Commonwealth University, Richmond, Virginia 23284
  • MR Author ID: 962672
  • ORCID: 0000-0003-1002-0286
  • Email:
  • Received by editor(s): February 28, 2022
  • Received by editor(s) in revised form: July 17, 2022
  • Published electronically: January 27, 2023
  • © Copyright 2023 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 376 (2023), 2641-2656
  • MSC (2020): Primary 14H40, 14H51, 14H10, 14C25; Secondary 14N15
  • DOI:
  • MathSciNet review: 4557877