Coherent systems of genus 0

2003/11/14 by H. Lange, Lange, H., P. E. Newstead +1 · 1 citation
Mathematics · #14F05 #14H60 #32L10 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14F05 #msc:14H60 #msc:32L10

paper · pdf · doi:10.48550/arxiv.math/0311239

15 pages

arxiv created 2003/11/14 · arxiv updated 2009/12/01

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.

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• Some moduli spaces of α-stable coherent systems on algebraic surfaces

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