109,556 research outputs found
Linear maps on nonnegative symmetric matrices preserving a given independence number
The independence number of a square matrix , denoted by , is
the maximum order of its principal zero submatrices. Let be the set
of nonnegative symmetric matrices with zero trace, and let be
the matrix with all entries equal to one. Given any integers
with , we prove that a linear map
satisfies and if and only if there is a permutation matrix
such that \phi(X)=P^TXP{~~~~\rm for~ all~}X\in S_n^+.$
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
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