On a Conjecture of Drinfeld

Abstract: Let $C$ be smooth irreducible projective curve of genus $g \ge 2$. Let $\mathcal{M}_C(n, \delta)$ be moduli space of stable vector bundles on $C$ of rank $n$ and fixed determinant $\delta$ of degree $d$. Then the locus of wobbly bundles are known to be closed in $\mathcal{M}_C(n, \delta)$. Drinfeld has conjectured that the wobbly locus is pure of co-dimension one, i.e., they form a divisor in $\mathcal{M}_C(n, \delta)$. In this article, we will give a prove of the conjecture.