We construct pointed Prym–Brill–Noether varieties parametrizing line bundles assigned to an irreducible étale double covering of a curve with prescribed minimal vanishing at fixed point. realize them as degeneracy loci in type D and deduce their classes case expected dimension. Thus, we determine Prym–Petri map prove version the theorem implying that dimension holds general case. These results ...

The dual of the category of pointed objects of a topos is semiabelian, thus is provided with a notion of semi-direct product and a corresponding notion of action. In this paper, we study various conditions for representability of these actions. First, we show this to be equivalent to the existence of initial normal covers in the category of pointed objects of the topos. For Grothendieck toposes...