A generalized Quot scheme and meromorphic vortices [article]

Indranil Biswas, Ajneet Dhillon, Jacques Hurtubise, Richard Wentworth
2014 arXiv   pre-print
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 : O^⊕ r_X → 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
more » ... m 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.
arXiv:1410.1182v1 fatcat:jnogo4s54bdd3dzvxfp77glf54