A generalized Quot scheme and meromorphic vortices

作者：Biswas Indranil^*; Dhillon Ajneet; Hurtubise Jacques; Wentworth Richard A

来源：Advances in Theoretical and Mathematical Physics, 2015, 19(4): 905-921.

DOI：10.4310/atmp.2015.v19.n4.a6

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-X(circle plus r) -> 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 Poincare polynomial of this compactification is computed.

• 出版日期2015
• 单位McGill