The determinant bundle on the moduli space of stable triples over a curve

Biswas, Indranil ; Raghavendra, N. (2002) The determinant bundle on the moduli space of stable triples over a curve Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 112 (3). pp. 367-382. ISSN 0253-4142

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Official URL: http://www.ias.ac.in/mathsci/vol112/aug2002/Pm1920...

Related URL: http://dx.doi.org/10.1007/BF02829790

Abstract

We construct a holomorphic Hermitian line bundle over the moduli space of stable triples of the form (E1, E2, Φ), where E1 and E2 are holomorphic vector bundles over a fixed compact Riemann surface X, and Φ: E2 → E1 is a holomorphic vector bundle homomorphism. The curvature of the Chern connection of this holomorphic Hermitian line bundle is computed. The curvature is shown to coincide with a constant scalar multiple of the natural Kahler form on the moduli space. The construction is based on a result of Quillen on the determinant line bundle over the space of Dolbeault operators on a fixed C Hermitian vector bundle over a compact Riemann surface.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Moduli Space; Stable Triples; Determinant Bundle; Quillen Metric
ID Code:3536
Deposited On:12 Oct 2010 04:18
Last Modified:16 May 2016 14:19

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