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 are considered, where is a parabolic Higgs bundle on a given compact Riemann surface X with parabolic structure on a fixed divisor S, and is a nonzero section of the underlying vector bundle. Sending such a triple to the Higgs bundle 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 . On the other hand, there is a map from the moduli space of stable parabolic triples to a Hilbert scheme , where Z denotes the total space of the line bundle , that sends a triple to the divisor defined by the section on the spectral curve corresponding to the parabolic Higgs bundle . Using this map and a meromorphic one-form on , 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 .