Mes anteior Día anterior Día siguiente Mes siguiente
Anual Mensual Semanal Hoy Buscar Ir al mes específico
Prelectura de tesis

Prelectura de tesis

Automorphisms of Higgs bundle Moduli spaces for real groups.

Manuel Jesus Perez Garca.

Advisor:  Oscar Garca Prada.

30 de Mayo, 16h., Sala 520, Módulo 17, Dpto. de Matemáticas

Abstract: Let G be a connected real form of a complex semisimple Lie
group GC with Lie algebra g. Let H be a maximal compact subgroup of
G and let  be a Cartan involution of g such that it induces a decompo-
sition into 1-eigenspaces g = h  m, where h is the Lie algebra of H. A
(G; )-Higgs bundle over a compact Riemann surface X is a pair consisting
on a holomorphic principal HC-bundle E and a holomorphic section ' of
E(mC) K where E(mC) is the bundle associated to E via the isotropy
representation C : HC ! GL(mC) and K is the canonical bundle over X.
Consider the moduli space M(G; ) of isomorphism classes of polystable
(G; )-Higgs bundles over X. In this talk we study the action of nite or-
der automorphisms of M(G) de ned by combining the multiplication of
the Higgs eld by an nth-root of unity and the action of an element in
(H1(X;Z(HC) Ker(C)) o Out(g; ))n, where Out(G; ) is the group of
outer automorphisms of G that commute with . In addition, we describe its
xed points subvarieties and, through non-abelian Hodge correspondence,
we translate these results to the moduli


Localización  30 de Mayo, 16h., Sala 520, Módulo 17, Dpto. de Matemáticas