Preprint 93/2001

Symplectic structures on moduli spaces of parabolic Higgs and Hilbert scheme

Indranil Biswas and Avijit Mukherjee

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Submission date: 27. Nov. 2001 (revised version: February 2003)
Pages: 15
published in: Communications in mathematical physics, 240 (2003) 1-2, p. 149-159 
DOI number (of the published article): 10.1007/s00220-003-0897-2
Bibtex
with the following different title: Symplectic structures on moduli spaces of parabolic Higgs bundles and Hilbert scheme
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Abstract:
Parabolic triples of the form formula12 are considered, where formula14 is a parabolic Higgs bundle on a given compact Riemann surface X with parabolic structure on a fixed divisor S, and formula20 is a nonzero section of the underlying vector bundle. Sending such a triple to the Higgs bundle formula14 a map from the moduli space of stable parabolic triples to the moduli space of stable parabolic Higgs bundles is obtained. The pull back, by this map, of the symplectic form on the moduli space of stable parabolic Higgs bundles will be denoted by formula24. On the other hand, there is a map from the moduli space of stable parabolic triples to a Hilbert scheme formula26, where Z denotes the total space of the line bundle formula30, that sends a triple formula12 to the divisor defined by the section formula20 on the spectral curve corresponding to the parabolic Higgs bundle formula14. Using this map and a meromorphic one-form on formula26, a natural two-form on the moduli space of stable parabolic triples is constructed. It is shown here that this form coincides with the above mentioned form formula24.

18.07.2014, 01:40