Globally F-regular type of moduli spaces and Verlinde formula

2018/02/23 by Xiaotao Sun, Sun, Xiaotao, Mingshuo Zhou +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Advanced Mathematical Identities

paper · pdf · doi:10.48550/arxiv.1802.08392

Abstract

We prove that moduli spaces of semistable parabolic bundles and generalized parabolic sheaves (GPS) with a fixed determinant on a smooth projective curve are globally F-regular type. As an application, we prove vanishing theorems on the moduli spaces of semistable parabolic sheaves on a singular curve, which combining with Factorization theorems in [24] and [25] give two recurrence relations among dimensions of spaces of generalized theta functions. By using of these recurrence relations, we prove an explicit formula (Verlinde formula) for the dimension of spaces of generalized theta functions.

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• Moduli space of homologically trivial parabolic (Higgs) bundles on the projective line and applications

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