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On moduli spaces of Hitchin pairs

Published online by Cambridge University Press:  18 July 2011

INDRANIL BISWAS ,
PETER B. GOTHEN  and
MARINA LOGARES
INDRANIL BISWAS
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India. e-mail: [email protected]
PETER B. GOTHEN
Affiliation:
Departamento de Matematica Pura, Facultade de Ciencias, Rua do Campo Alegre 687, 4169-007 PortoPortugal. e-mail: [email protected]
MARINA LOGARES
Affiliation:
Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Serrano 113 Bis 28006 Madrid. Spain. e-mail: [email protected]
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Abstract

Let X be a compact Riemann surface X of genus at–least two. Fix a holomorphic line bundle L over X. Let be the moduli space of Hitchin pairs (E, φ ∈ H0(End0(E) ⊗ L)) over X of rank r and fixed determinant of degree d. The following conditions are imposed:

  1. (i) deg(L) ≥ 2g−2, r ≥ 2, and L⊗rKX⊗r;

  2. (ii) (r, d) = 1; and

  3. (iii) if g = 2 then r ≥ 6, and if g = 3 then r ≥ 4.

We prove that that the isomorphism class of the variety uniquely determines the isomorphism class of the Riemann surface X. Moreover, our analysis shows that is irreducible (this result holds without the additional hypothesis on the rank for low genus).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 151 , Issue 3 , November 2011 , pp. 441 - 457
Copyright
Copyright © Cambridge Philosophical Society 2011

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