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COHERENT SYSTEMS ON ELLIPTIC CURVES

H. LANGE

Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstrasse 1½, D-91054 Erlangen, Germany

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and

P. E. NEWSTEAD

Department of Mathematical Sciences, University of Liverpool, Peach Street, Liverpool L69 7ZL, UK

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https://doi.org/10.1142/S0129167X05003090Cited by:13 (Source: Crossref)

Abstract

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

Keywords:

AMSC: Primary 14H60, Secondary 14F05, Secondary 32L10

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