483 research outputs found
The Weil-Petersson current for moduli of vector bundles and applications to orbifolds
We investigate stable holomorphic vector bundles on a compact complex
K\"ahler manifold and more generally on an orbifold that is equipped with a
K\"ahler structure. We use the existence of Hermite-Einstein connections in
this set-up and construct a generalized Weil-Petersson form on the moduli space
of stable vector bundles with fixed determinant bundle. We show that the
Weil-Petersson form extends as a (semi-)positive closed current for
degenerating families that are restrictions of coherent sheaves. Such an
extension will be called a Weil-Petersson current. When the orbifold is of
Hodge type, there exists a determinant line bundle on the moduli space; this
line bundle carries a Quillen metric, whose curvature coincides with the
generalized Weil-Petersson form. As an application we show that the determinant
line bundle extends to a suitable compactification of the moduli space.Comment: To appear in Annales de la Facult\'e des Sciences de Toulouse.
Math\'ematiques. Abstract added, typos correcte
Geometry of moduli spaces of Higgs bundles
We construct a Petersson-Weil type K\"ahler form on the moduli spaces of
Higgs bundles over a compact K\"ahler manifold. A fiber integral formula for
this form is proved, from which it follows that the Petersson-Weil form is the
curvature of a certain determinant line bundle, equipped with a Quillen metric,
on the moduli space of Higgs bundles over a projective manifold. The curvature
of the Petersson-Weil K\"ahler form is computed. We also show that, under
certain assumptions, a moduli space of Higgs bundles supports of natural
hyper-K\"ahler structure.Comment: To appear in Communications in Analysis and Geometr
Estimates of Weil-Petersson volumes via effective divisors
We study the asymptotics of the Weil-Petersson volumes of the moduli spaces
of compact Riemann surfaces of genus with punctures, for fixed as
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