Advances in Theoretical and Mathematical Physics

Volume 19 (2015)

Number 4

A generalized Quot scheme and meromorphic vortices

Pages: 905 – 921

DOI: http://dx.doi.org/10.4310/ATMP.2015.v19.n4.a6

Authors

Indranil Biswas (School of Mathematics, Tata Institute of Fundamental Research, Bombay, India)

Ajneet Dhillon (Department of Mathematics, Middlesex College, University of Western Ontario, London, Ontario, Canada)

Jacques Hurtubise (Department of Mathematics, McGill University, Montreal, Quebec, Canada)

Richard A. Wentworth (Department of Mathematics, University of Maryland, College Park, Md., U.S.A.)

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\[f : \mathcal{O}^{\oplus r}_{X} \longrightarrow \mathcal{F}\]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 $(\mathcal{F}_1, f_1)$ and $(\mathcal{F}_2, f_2)$ are called isomorphic if there is a holomorphic isomorphism of $\mathcal{F}_1)$ with $\mathcal{F}_2$ 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.

Full Text (PDF format)