The parabolic Verlinde formula: iterated residues and wall-crossings

Szenes, András¹ ; Trapeznikova, Olga¹

¹ Section de mathématiques, Université de Genève, Geneva, Switzerland

Geometry & topology, Tome 28 (2024) no. 5, pp. 2259-2311.

Résumé

We give a new proof for the parabolic Verlinde formula in all ranks based on a comparison of wall-crossings in geometric invariant theory and certain iterated residue functionals. On the way, we develop a tautological variant of Hecke correspondences, calculate the Hilbert polynomials of the moduli spaces, and present a new, transparent, local approach to the $\rho$–shift problem of the theory.

Détail

DOI : 10.2140/gt.2024.28.2259

Keywords: Verlinde formula, wall-crossing, parabolic bundles

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