Infinitesimal deformations of the tangent bundle of a moduli space of vector bundles over a curve

Biswas, Indranil

Osaka J. Math., Tome 43 (2006) no. 2, p. 263-274 / Harvested from Project Euclid

Résumé

Fix a line bundle $\xi$ on a connected smooth complex projective curve $X$ of genus at least three. Let $\mathcal{N}$ denote the moduli space of all stable vector bundles over $X$ of rank $n$ and determinant $\xi$. We assume that $n\geq 3$ and coprime to $\operatorname{degree}(\xi)$; If $\operatorname{genus}(X)\leq 4$, then we also assume that $n \geq 4$. We prove that $H^i(\mathcal{N}, \End(T\mathcal{N}\mkern2mu)) = H^i(X, \mathcal{O}_X)$ for $i= 0,1$.

Publié le : 2006-06-14
Classification: 14D20, 14F05

@article{1152203940,
     author = {Biswas, Indranil},
     title = {Infinitesimal deformations of the tangent bundle of a moduli space of vector bundles over a curve},
     journal = {Osaka J. Math.},
     volume = {43},
     number = {2},
     year = {2006},
     pages = { 263-274},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1152203940}
}

Biswas, Indranil. Infinitesimal deformations of the tangent bundle of a moduli space of vector bundles over a curve. Osaka J. Math., Tome 43 (2006) no. 2, pp.  263-274. http://gdmltest.u-ga.fr/item/1152203940/