# Plucker forms and the theta map - Mathematics > Algebraic Geometry

Abstract: In this paper we introduce the elementary notion of Pl\-ucker form of a pair$E,S$, where $E$ is a vector bundle of rank $r$ on a smooth, irreducible,complex projective variety $X$ and $S \subset H^0E$ is a subspace ofdimension $rm$. We apply this notion to the study of theta map $\theta r$ onthe moduli space $SU Xr,0$ of semistable vector bundles of rank $r$ andtrivial determinant on a curve $X$ of genus $g$. We prove that $\theta r$ isgenerically injective if $X$ is general and $g >> r$.

Author: Sonia Brivio, Alessandro Verra

Source: https://arxiv.org/