Birational maps of moduli of Brill-Noether pairs

Abstract

Let $C$ be a smooth projective irreducible curve of genus $g$. And let $G_{\alpha }(n,d,l)$ be the moduli space of $\alpha$ stable pairs of a vector bundle of $\rank n, °d$ and a subspace of $H^0(C,E)$ of $\dim =l$. We find an explicit birational map from $G_{\alpha }(n,d,n+1)$ to $G_{\alpha }(1,d,n+1)$ for $C$ general, $1/\alpha \gg 0$ and $g\ge n^2-1$. Because of this and other examples, we conjecture $G_{\alpha }(a,d,a+z)$ maps birationally to $G_{\alpha }(z,d,a+z)$ for $1/\alpha \gg 0$ and $C$ general with $g>2$.

12 pp

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