Two-pointed Prym-Brill-Noether Loci and coupled Prym-Petri theorem

TL;DR

This paper develops a new two-pointed Prym-Brill-Noether theory, determining K-theory classes and establishing a Prym-Petri theorem with special vanishing conditions at two points, extending previous unpointed and pointed results.

Contribution

It introduces two-pointed Prym-Brill-Noether loci with explicit K-theory classes and proves a Prym-Petri theorem in the two-pointed setting, generalizing prior work.

Findings

Derived K-theory classes for two-pointed loci.

Established a two-pointed Prym-Petri theorem.

Extended unpointed and pointed Prym results to two points.

Abstract

We establish two-pointed Prym-Brill-Noether loci with special vanishing at two points, and determine their K-theory classes when the dimensions are as expected. The classes are derived by the applications of a formula for the K-theory of certain vexillary degeneracy loci in type D. In particular, we show a two-pointed version of Prym-Petri theorem on the expected dimension in the general case, with a coupled Prym-Petri map. Our approach is inspired by the work on pointed cases by Tarasca, and we generalize unpointed cases by De Concini-Pragacz and Welters.