A generalized Quot scheme and meromorphic vortices

الأصل · EN

Let X be a compact connected Riemann surface. Fix a positive integer r and two nonnegative integers dₚ and dz. Consider all pairs of the form (F, f), where F is a holomorphic vector bundle on X of rank r and degree dz-dₚ, and f: O⊕ ʳₓ → F is a meromorphic homomorphism which an isomorphism outside a finite subset of X and has pole (respectively, zero) of total degree dₚ (respectively, dz). Two such pairs (F₁, f₁) and (F₂, f₂) are called isomorphic if there is a holomorphic isomorphism of F₁ with F₂ over X that takes f₁ to f₂. We construct a natural compactification of the moduli space equivalence classes pairs of the above type. The Poincaré polynomial of this compactification is computed.