On linear systems and a conjecture of D. C. Butler

U. N. Bhosle, L. Brambila-Paz, P. E. Newstead

Published 2013-04-16, updated 2014-12-30Version 4

Let $C$ be a smooth irreducible projective curve of genus $g$ and $L$ a line bundle of degree $d$ generated by a linear subspace $V$ of $H^0(L)$ of dimension $n+1$. We prove a conjecture of D. C. Butler on the semistability of the kernel of the evaluation map $V\otimes{\mathcal O}_C\to L$ and obtain new results on the stability of this kernel. The natural context for this problem is the theory of coherent systems on curves and our techniques involve wall crossing formulae in this theory.