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

Abstract

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.

Final version accepted for publication in Internat. J. math

References in corpus (1)

• Stability of line bundles transforms on curves with respect to low codimensional subspaces

Cited by in corpus (6)

• On kernel bundles over reducible curves with a node
• Towards the Bertram-Feinberg-Mukai Conjecture
• Coherent systems on curves of compact type
• Tangent cones to generalised theta divisors and generic injectivity of the theta map
• Segre invariant and a stratification of the moduli space of coherent systems
• A Riemann--Kempf singularity theorem for higher rank Brill--Noether loci