A generalized Quot scheme and meromorphic vortices

2014/10/05 by Indranil Biswas, Biswas, Indranil, Ajneet Dhillon +5
Mathematics · #14D21 #14D23 #14H60 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1410.1182

openalex publication_date 2014/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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^{⊕ 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 (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.

Related

• Automorphisms of the Quot schemes associated to compact Riemann surfaces
• Quot schemes and Ricci semipositivity
• Automorphisms of the generalized quot schemes
• Gromov Invariants for Holomorphic Maps from Riemann Surfaces to Grassmannians
• Isomorphism of compactifications of moduli of vector bundles: nonreduced moduli