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

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

2007-12-13

arxiv.org/abs/0712.2215v1

Mathematics

Algebraic Geometry

33 pages

Scientific paper

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 $\alpha$. We determine the top critical value of $\alpha$ and show that the corresponding ``flip'' has positive codimension. We investigate also the non-emptiness of the moduli space for smaller values of $\alpha$, proving in many cases that the condition for non-emptiness is the same as for large $\alpha$. 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.

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