The Abel-Jacobi isomorphism on one cycles on the moduli space of vector bundles with trivial determinant on a curve

Abstract

We consider the moduli space $\cSU_C^s(r,\cO_C)$ of rank r stable vector bundles with trivial determinant on a smooth projective curve $C$ of genus $g$. We show that the Abel-Jacobi map on the rational Chow group $CH_1(\cSU_C^s(r,\cO_C))_{hom}\otimes \Q$ of one cycles which are homologous to zero, is an isomorphism onto the bottom weight intermediate Jacobian, which is identified with the Jacobian $Jac(C)\otimes \Q$. The result holds whenever $r\geq 2$ and $g\geq 4$.