9,800 research outputs found
Flat -Connections, Mochizuki Correspondence and Twistor Spaces
In this paper, we first collect some basic results for -flat
bundles, and then get an estimate for the norm of -flat sections,
which leads to some vanishing theorem. Mochizuki correspondence provides a
homeomorphism between the moduli space of (poly-)stable -flat bundles
and that of (poly-)stable Higgs bundles, and provides a dynamical system on the
later moduli space (the Dolbeault moduli space). We investigate such dynamical
system, in particular, we discuss the corresponding first variation and
asymptotic behavior. We generalize the Deligne's twistor construction for any
element of the outer automorphism group of the fundamental group of
Riemann surface to obtain the -twistor space, and we apply the twistor
theory to study a Lagrangian submanifold of the de Rham moduli space. As an
application, we prove a Torelli-type theorem for the twistor spaces, and
meanwhile, we prove that the oper stratum in the oper stratification of the de
Rham moduli space is the unique closed stratum of minimal dimension, which
partially confirms a conjecture by Simpson.Comment: Simpson pointed out a mistake on the Moishezon property for the
twistor space in the last version, we delete it and add a section on the
study of oper stratification of the de Rham moduli space as an applicatio
The Hitchin--Kobayashi Correspondence for Quiver Bundles over Generalized K\"ahler Manifolds
In this paper, we establish the Hitchin--Kobayashi correspondence for the
-holomorphic quiver bundle over a compact
generalized K\"{a}hler manifold such that is Gauduchon
with respect to both and , namely is
-polystable if and only if admits an
-Hermitian--Einstein metric.Comment: To appear in The Journal of Geometric Analysi
Asymptotics in randomized urn models
This paper studies a very general urn model stimulated by designs in clinical
trials, where the number of balls of different types added to the urn at trial
n depends on a random outcome directed by the composition at trials
1,2,...,n-1. Patient treatments are allocated according to types of balls. We
establish the strong consistency and asymptotic normality for both the urn
composition and the patient allocation under general assumptions on random
generating matrices which determine how balls are added to the urn. Also we
obtain explicit forms of the asymptotic variance-covariance matrices of both
the urn composition and the patient allocation. The conditions on the
nonhomogeneity of generating matrices are mild and widely satisfied in
applications. Several applications are also discussed.Comment: Published at http://dx.doi.org/10.1214/105051604000000774 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Non-Archimedean meromorphic solutions of functional equations
In this paper, we discuss meromorphic solutions of functional equations over
non-Archimedean fields, and prove analogues of the Clunie lemma, Malmquist-type
theorem and Mokhon'ko theorem
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