A pointed Prym-Petri Theorem

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 and De Concini-Pragacz 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, extending to the Prym setting work of Ortega.

Euler Characteristics of Brill-Noether Loci on Prym Varieties

“…Indeed Theorem 1.2 extends the formulas for the cohomology classes of the Brill-Noether loci of Prym varieties by Concini and Pragacz [8]. When it comes to β = 0, we recover the class of the pointed Brill-Noether loci for Prym varieties, Corollary 4.3 that coincides with the recent work of Tarasca [24,Theorem 1].…”

“…While working this paper, the author learned from private conversation with David Anderson that Corollary 4.3 was be found independently in [24,Theorem 1]. To be rigorous, we take this occasion to provide a more detailed proof, as the proof of [24, Theorem 1] was sketched.…”