Martens and Mumford theorems for higher rank Brill--Noether loci

Parviz Asefi Nazarlou, Ali Bajravani, George H. Hitching

Generalizing the Martens theorem for line bundles over a curve $C$, we obtain upper bounds on the dimension of the Brill--Noether locus $B_{n,d}^k$ parametrizing stable bundles of…