## A pointed Prym–Petri Theorem

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## Abstract:

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].## References

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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: tarascan@vcu.edu
- 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: https://doi.org/10.1090/tran/8792
- MathSciNet review: 4557877