On the Image of Certain Extension Maps. I

Mejía, Israel Moreno

Canadian mathematical bulletin, Tome 50 (2007) no. 3, pp. 427-433

Résumé

Let $X$ be a smooth complex projective curve of genus $g\ge 1$ . Let $\xi \in {{J}^{1}}\left( X \right)$ be a line bundle on $X$ of degree 1. Let $W=\text{Ex}{{\text{t}}^{1}}\left( {{\xi }^{n}},{{\xi }^{-1}} \right)$ be the space of extensions of ${{\xi }^{n}}$ by ${{\xi }^{-1}}$ . There is a rational map ${{D}_{\xi }}:G\left( n,W \right)\to S{{U}_{X}}\left( n+1 \right)$ , where $G\left( n,W \right)$ is the Grassmannian variety of $n$ -linear subspaces of $W$ and $S{{U}_{X}}\left( n+1 \right)$ is the moduli space of rank $n+1$ semi-stable vector bundles on $X$ with trivial determinant. We prove that if $n=2$ , then ${{D}_{\xi }}$ is everywhere defined and is injective.

Détail

DOI : 10.4153/CMB-2007-041-0

Mots-clés : 14H60, 14F05, 14D20