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arXiv · 2210.12764

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

Ali Bajravani
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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 $B^k_{2, d}$ is of expected dimension, then we prove that its smoothness is equivalent with the smoothness of $B^{k}_{2, d+1}$.

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Ali Bajravani. 2022-10-23. Excess dimensions of Brill--Noether schemes of rank two stable bundles. https://arxiv.org/abs/2210.12764

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