Poincare sheaves on the moduli spaces of torsionfree sheaves over an irreducible curve

2011/08/07 by Usha N. Bhosle, Indranil Biswas, Bhosle, Usha N. +1
Mathematics · #14D20 #14F05 #14P99 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14D20 #msc:14F05 #msc:14P99

paper · pdf · doi:10.48550/arxiv.1108.1528

To appear in Communications in Algebra

arxiv created 2011/08/07 · arxiv updated 2011/08/09

Abstract

Let Y be a geometrically irreducible reduced projective curve defined over real numbers. Let U_Y (respectively, U'_Y) be the moduli space of geometrically stable torsionfree sheaves (respectively, locally free sheaves) on Y of rank n and degree d. Define χ = d+n(1-genus(Y)), where genus(Y) is the arithmetic genus. If 2n is coprime to χ, then there is a Poincare sheaf over U_Y× Y. If 2n is not coprime to χ, then there is no Poincare sheaf over any nonempty open subset of U'_Y.

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