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

2007/12/13 by Bhosle, U. N., Brambila-Paz, L., Newstead, P. E. · 3 citations
#14H60 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0712.2215

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 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≤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.

Cited by

• Derived category of coherent systems on curves and stability conditions
• Geometry of linearly stable coherent systems over curves
• Stability of syzygy bundles over certain curves of compact type

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