Work

Six dimensional solvmanifolds with holomorphically trivial canonical bundle

Year: 2014

Type: article

Abstract: We determine the 6-dimensional solvmanifolds admitting an invariant complex structure with holomorphically trivial canonical bundle. Such complex structures are classified up to isomorphism, and the existence of strong Kähler with torsion (SKT), generalized Gauduchon, balanced and strongly Gauduchon metrics is studied. As an application we construct a holomorphic family $(M,J_a)$ of compact complex manifolds such that $(M,J_a)$ satisfies the $\partial\bar\partial$-Lemma and admits a balanced metric for any $a\not=0$, but the central limit neither satisfies the $\partial\bar\partial$-Lemma nor admits balanced metrics.

Source: LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas)

DOI: 10.48550/arxiv.1401.0512

Authors: Fino, Anna, Otal, Antonio, Ugarte, Luis

Institutions: Centro Universitario de la Defensa Zaragoza, University of Turin, Universidad de Zaragoza

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Ministerio de Ciencia e Innovación, Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni

Award: G4362435372