148,170 research outputs found
Matrix Representations of Holomorphic Curves on
We construct a matrix representation of compact membranes analytically
embedded in complex tori. Brane configurations give rise, via Bergman
quantization, to U(N) gauge fields on the dual torus, with
almost-anti-self-dual field strength. The corresponding U(N) principal bundles
are shown to be non-trivial, with vanishing instanton number and first Chern
class corresponding to the homology class of the membrane embedded in the
original torus. In the course of the investigation, we show that the proposed
quantization scheme naturally provides an associative star-product over the
space of functions on the surface, for which we give an explicit and
coordinate-invariant expression. This product can, in turn, be used the
quantize, in the sense of deformation quantization, any symplectic manifold of
dimension two.Comment: 29 page
Connections on parahoric torsors over curves
We define parahoric \cG--torsors for certain Bruhat--Tits group scheme
\cG on a smooth complex projective curve when the weights are real, and
also define connections on them. We prove that a \cG--torsor is given by a
homomorphism from to a maximal compact subgroup of ,
where is the parabolic divisor, if and only if the torsor is
polystable.Comment: To appear in Publ.RIMS, Kyoto Uni
The Nori-Hilbert scheme is not smooth for 2-Calabi Yau algebras
Let be an algebraically closed field of characteristic zero and let
be a finitely generated algebra. The Nori - Hilbert scheme of ,
parameterizes left ideals of codimension in and it is well known to be
smooth when is formally smooth. In this paper we will study the Nori -
Hilbert scheme for Calabi Yau algebras. The main examples of these are
surface group algebras and preprojective algebras. For the former we show that
the Nori-Hilbert scheme is smooth for only, while for the latter we show
that the smooth components that contain simple representations are precisely
those that only contain simple representation. Under certain conditions we can
generalize this last statement to arbitrary Calabi Yau algebras.Comment: 30 pages, research paper. Accepted for publication in Journal of
Noncommutative Geometr
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