Plucker forms and the theta map

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 $S\subset H^0(E)$ is a subspace of dimension $rm$. We apply this notion to the study of theta map ${\theta }_r$ on the moduli space $S{U}_X(r,0)$ of semistable vector bundles of rank $r$ and trivial determinant on a curve $X$ of genus $g$. We prove that ${\theta }_r$ is generically injective if $X$ is general and $g>>r$.

20 pages to appear on "American Journal of Mathematics"

Cited by in corpus (1)

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