Bounds on the dimension of the Brill–Noether schemes of rank two bundles
The aim of this note is to find upper bounds on the dimension of Brill–Noether locus inside the moduli space of rank two vector bundles on a smooth algebraic curve. We deduce some consequences of these bounds.
KeywordsBrill–Noether theory Petri map Vector bundles
Mathematics Subject Classification14H51 14H60
The author wishes to thank F. Flamini, P. Newstead, and M. Teixidor for their valuable hints and for sharing their knowledge. I specially thank G. H. Hitching whose careful reading and comments changed the previous manuscript of this paper, considerably. Teixidor supported me by sending a draft of the unpublished paper  at the right time; to her, I express my double gratitude. I also thank the anonymous referee for his/her very useful comments on the paper.
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