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COHERENT SYSTEMS OF GENUS 0

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/S0129167X04002326Cited by:11 (Source: Crossref)

Abstract

In this paper we begin the classification of coherent systems (E,V) on the projective line which are stable with respect to some value of a parameter α. In particular we show that the moduli spaces, if non-empty, are always smooth and irreducible of the expected dimension. We obtain necessary conditions for non-emptiness and, when dim V=1 or 2, we determine these conditions precisely. We also obtain partial results in some other cases.

Keywords:

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

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