Resumen de On the Image of Certain Extension Maps. I

Israel Moreno-Mejía

• Let X be a smooth complex projective curve of genus g \geq 1. Let xi \in J1(X) be a line bundle on X of degree 1. Let W = Ext1(xin, xi-1) be the space of extensions of xin by xi-1. There is a rational map Dxi : G(n,W) \rightarrow SUX(n+1), where G(n,W) is the Grassmannian variety of n-linear subspaces of W and SUX(n+1) is the moduli space of rank n + 1 semi-stable vector bundles on X with trivial determinant. We prove that if n = 2, then Dxi is everywhere defined and is injective.