We construct pointed Prym-Brill-Noether varieties parametrizing line bundles assigned to an irreducible e ' tale double covering of a curve with a prescribed minimal vanishing at a fixed point. We realize them as degen-eracy 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. ecole 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 va-rieties 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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