On the Image of Certain Extension Maps. I

• Autores: Israel Moreno-Mejía
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 50, Nº 3, 2007, págs. 427-433
• Idioma: inglés
• DOI: 10.4153/cmb-2007-041-0
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• Resumen

  • 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.