Excess dimensions of Brill--Noether schemes of rank two stable bundles

Abstract

We use results of M. Aprodu and E. Sernesi to extend a result by Fulton--Harris--Lazarsfeld in Brill--Noether theory of line bundles %and, as well, a result by Aprod-Sernesi in theory of Secant Loci, to Brill--Noether loci of stable bundles inside the moduli space of rank two stable vector bundles on a smooth projective algebraic curve. As a consequence; if $B_{2,d}^k$ is of expected dimension, then we prove that its smoothness is equivalent with the smoothness of $B_{2,d+1}^k$.

arXiv admin note: substantial text overlap with arXiv:2101.06681