On coherent systems of type (n,d,n+1) on Petri curves

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

On coherent systems of type (n,d,n+1) on Petri curves

Authors

Bhosle, U. N.

Brambila-Paz, L.

Newstead, P. E.

Description

We study coherent systems of type $(n,d,n+1)$ on a Petri curve $X$ of genus $g\ge2$. We describe the geometry of the moduli space of such coherent systems for large values of the parameter $α$. We determine the top critical value of $α$ and show that the corresponding ``flip'' has positive codimension. We investigate also the non-emptiness of the moduli space for smaller values of $α$, proving in many cases that the condition for non-emptiness is the same as for large $α$. We give some detailed results for $g\le5$ and applications to higher rank Brill-Noether theory and the stability of kernels of evaluation maps, thus proving Butler's conjecture in some cases in which it was not previously known.
33 pages