A generalized Quot scheme and meromorphic vortices

Indranil Biswas; Ajneet Dhillon; Jacques Hurtubise; Richard Wentworth

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arXiv · 1410.1182

A generalized Quot scheme and meromorphic vortices

Indranil Biswas·Ajneet Dhillon·Jacques Hurtubise·Richard Wentworth

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Abstract

Let X be a compact connected Riemann surface. Fix a positive integer r and two nonnegative integers d_p and d_z. Consider all pairs of the form (F, f), where F is a holomorphic vector bundle on X of rank r and degree d_z-d_p, and f : {\mathcal O}^{\oplus r}_X \rightarrow F is a meromorphic homomorphism which an isomorphism outside a finite subset of X and has pole (respectively, zero) of total degree d_p (respectively, d_z). Two such pairs $(F_1, f_1) and $(F_2, f_2) are called isomorphic if there is a holomorphic isomorphism of F_1 with F_2 over X that takes f_1 to f_2. We construct a natural compactification of the moduli space equivalence classes pairs of the above type. The Poincaré polynomial of this compactification is computed.

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BibTeX RIS

Indranil Biswas, Ajneet Dhillon, Jacques Hurtubise, Richard Wentworth. 2014-10-05. A generalized Quot scheme and meromorphic vortices. https://arxiv.org/abs/1410.1182

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