Enumerative geometry on the moduli space of rank 2 Higgs bundles

Diplôme Thèse Enumerative geometry on the moduli space of rank 2 Higgs bundles eng 2020-08-20 author Chiarello Simone Melchiorre 838121 director Szenes Andras 664272 10.13097/archive-ouverte/unige:150031 urn:nbn:ch:unige-1500315 Sc. 5515 The P=W conjecture identifies the perverse filtration of the Hitchin system on the cohomology of the moduli space of Higgs bundles with the weight filtration of the corresponding character variety. In this paper, we introduce an enumerative approach to to this problem; our technique only uses the structure of the equivariant intersection numbers on the moduli space of Higgs bundles, and little information about the topology of the Hitchin map. In the rank 2 case, starting from the known intersection numbers of the moduli of stable bundles, we derive the equivariant intersection numbers on the Higgs moduli, and then verify the top perversity part of our enumerative P=W statement for even tautological classes. A key in this calculation is the existence of polynomial solutions to the Discrete Heat Equation satisfying particular vanishing properties. For odd classes, we derive a determinantal criterion for the enumerative P=W. Higgs Bundles Enumerative Geometry Algebraic P=W Intersection theory Dewey 510 25 Section de mathématiques 11 false 0ac268d7-a77e-4dc8-8526-035602389de4 Thesis Public Finalversion.pdf 676359 application/pdf a5226b63-ed9e-43eb-b3c8-7f42f20d8d4b Agreement Private Chiarello-SimoneMelchiorre_Contrat_.pdf 491097 application/pdf cc00dd0725b9b97ed77fafa824a51aa0bced3c73bbcda9872cde7a248425c98c 9ba1ec56-9813-4d35-b6ae-3ff2ba7a3413 Publication mode Private Chiarello-SimoneMelchiorre_Mode-de-.pdf 467029 application/pdf openAccess Faculté des sciences / Section de mathématiques

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Enumerative geometry on the moduli space of rank 2 Higgs bundles				2020	413	236

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Chiarello, Simone Melchiorre