Wall-crossings for moduli spaces of parabolic bundles on curves

Diplôme Thèse Wall-crossings for moduli spaces of parabolic bundles on curves eng 2023 2023 author Trapeznikova Olga 0000-0002-1034-3969 910994 director Szenes Andras 664272 Section de mathématiques (MATH) 10.13097/archive-ouverte/unige:172123 urn:nbn:ch:unige-1721239 Sc. 5755 The Verlinde formula, an expression for the Euler characteristic of line bundles on the moduli spaces of stable bundles on a curve, is a strikingly beautiful statement in enumerative geometry motivated by quantum physics. It has attracted a lot of attention over the years, and has a number of different proofs. In Chapter 2 of this thesis, we give a new proof of the more difficult parabolic variant of this formula based on a comparison of wall-crossings in Geometric Invariant Theory and certain iterated residues calculus. On the way, we develop a tautological variant of Hecke correspondences, calculate the Hilbert polynomials of the moduli spaces, and present a new, transparent approach to the rho-shift problem of the theory. In Chapter 3 we show that the residue/wall-crossing methods of Chapter 2 may be successfully employed to describe the pushforward maps in the K-theory of moduli spaces and present new, explicit formulas for the Euler characteristic of a wider class of vector bundles on the moduli space of stable parabolic bundles. Our work was motivated by the results of Teleman and Woodward on the index of K- theory classes of moduli stacks. Dewey 510 25 Section de mathématiques 11 false 080ef2e0-839f-4c16-b0b6-3bcc109758e9 Thesis Public Thesis 5755.pdf 1296093 application/pdf 521c9de5d7e190894638c2322d34faa0fd83381e88672dfa44f4cccd441976d4 8b79cdc3-3b2a-466c-b237-713855866103 Imprimatur Public Imprimature.pdf 120815 application/pdf 58ff5e89c9a9c79ebb79fd5f75ca8d61449bff4c365aa48a16bedb62201c3497 openAccess Faculté des sciences / Section de mathématiques

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Wall-crossings for moduli spaces of parabolic bundles on curves				2023	434	1,409

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Trapeznikova, Olga

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