Coherent Systems on Elliptic curves

Details Coherent Systems on Elliptic curves Coherent Systems on Elliptic curves

2004-11-03

arxiv.org/abs/math/0411064v3

Mathematics

Algebraic Geometry

Final version with some improvements in the presentation and an additional reference

Scientific paper

In this paper we consider coherent systems $(E,V)$ on an elliptic curve which are stable with respect to some value of a parameter $\alpha$. We show that the corresponding moduli spaces, if non-empty, are smooth and irreducible of the expected dimenson. Moreover we give precise conditions for non-emptiness of the moduli spaces. Finally we study the variation of the moduli spaces with $\alpha$.

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