Two‐pointed Prym–Brill–Noether loci and coupled Prym–Petri theorem

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 the 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.