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Deformations of the generalised Picard bundle

I. Biswas·L. Brambila-Paz·P. E. Newstead
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Abstract

Let X be a non-singular algebraic curve of genus at least 3 and let M denote the moduli space of stable vector bundles of rank n and fixed determinant of degree d with n and d coprime. For any semistable bundle E over X, we can pull E back to XxM, tensor with a universal bundle and take the direct image W(E) on M. If the degree of E is sufficiently large, this direct image is locally free and we call it a generalised Picard bundle. In this paper we prove an inversion formula allowing us to recover E from W(E) and compute the space of infinitesimal deformations of W(E). We also identify a family of deformations which is locally complete and frequently globally complete as well. The paper as a whole is a generalisation of results of Kempf and Mukai on Picard bundles over the Jacobian of X.

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I. Biswas, L. Brambila-Paz, P. E. Newstead. 2003-08-29. Deformations of the generalised Picard bundle. https://arxiv.org/abs/math/0308292

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