Special Hermitian metrics, complex nilmanifolds and holomorphic deformations

This paper considers compact complex manifolds with special Hermitian metrics, mainly balanced and strongly Gauduchon metrics. The main aim is to study the interaction of several complex invariants of cohomological type and metric properties of compact complex manifolds, as well as their behavior un...

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Detalles Bibliográficos
Autor: Ugarte Vilumbrales, Luis
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2014
País:España
Institución:Universidad de Zaragoza
Repositorio:Zaguán. Repositorio Digital de la Universidad de Zaragoza
OAI Identifier:oai:zaguan.unizar.es:165747
Acceso en línea:http://zaguan.unizar.es/record/165747
Access Level:acceso abierto
Descripción
Sumario:This paper considers compact complex manifolds with special Hermitian metrics, mainly balanced and strongly Gauduchon metrics. The main aim is to study the interaction of several complex invariants of cohomological type and metric properties of compact complex manifolds, as well as their behavior under holomorphic deformation of the complex structure. It is proved that the class of complex nilmanifolds provides a very rich source of explicit examples of analytic families of compact complex manifolds with interesting and unusual behaviors in their central fibers. It is shown that the complex geometry of the 6-dimensional manifold which is the product of two copies of the Heisenberg nilmanifold allows one to construct a holomorphic deformation with interesting properties in its central limit.

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