On Poincare bundles of vector bundles on curves

Abstract

Let $M$ denote the moduli space of stable vector bundles of rank $n$ and fixed determinant of degree coprime to $n$ on a non-singular projective curve $X$ of genus $g\ge 2$. Denote by $\cU$ a universal bundle on $X\times M$. We show that, for $x,y\in X,x\ne y$, the restrictions $\cU|\{x\} \times M$ and $\cU|\{y\} \times M$ are stable and non-isomorphic when considered as bundles on $X$.

8 pages