Plucker forms and the theta map

2009/10/29 by Brivio, Sonia, Verra, Alessandro
#14 H 60 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0910.5630

Abstract

In this paper we introduce the elementary notion of Plücker form of a pair (E,S), where E is a vector bundle of rank r on a smooth, irreducible, complex projective variety X and S ⊂ H⁰(E) is a subspace of dimension rm. We apply this notion to the study of theta map θ_r on the moduli space SU_X(r,0) of semistable vector bundles of rank r and trivial determinant on a curve X of genus g. We prove that θ_r is generically injective if X is general and g >> r.

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