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Deformations of the Picard Bundle

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

Let X be a nonsingular projective algebraic curve of genus g\ge3. We consider the moduli space M of stable bundles of fixed determinant with rank n and degree d coprime and d>n(2g-2). There is a universal bundle on XxM and we consider the direct image of this bundle on M. With the given restriction on d, this is a bundle W called the Picard bundle. Our main object in this paper is to compute the infinitesimal deformations of W. We show also that W possesses a moduli space and that the connected component of this moduli space containing W is isomorphic as a polarised variety to the Jacobian of X.

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I. Biswas, L. Brambila-Paz, P. E. Newstead. 2002-06-10. Deformations of the Picard Bundle. https://arxiv.org/abs/math/0104170

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