Six-Dimensional Solvmanifolds with Holomorphically Trivial Canonical Bundle

By Anna Fino, A. Otal, L. Ugarte. 2014

47 citations recorded by the source corpus.

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 K\"ahler 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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2c5fd45788575c2265e8811f4ef87c4a0fdd2dc3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Romina M. Arroyo
2. Ramiro A. Lafuente
3. Fabio Paradiso
4. Anna Fino
5. Michael Jablonski

In Geometry and Topology

1. Romina M. Arroyo
2. Ramiro A. Lafuente
3. Fabio Paradiso
4. Anna Fino
5. Michael Jablonski

Citations in the corpus

• The long‐time behavior of the homogeneous pluriclosed flow (2017, background): “In dimension 6, all nilpotent examples were classified in [9] (see also [34]), and some partial results on the solvable case are given in [8].”