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

Abstract

We study coherent systems of type (n, d, n + 1) on a Petri curve X of genus g ≥ 2. We describe the geometry of the moduli space of such coherent systems for large values of the parameter a. We determine the top critical value of a 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 a. We give some detailed results for g ≤ 5 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.