

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 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
.