Fano manifolds of Calabi-Yau type

TL;DR

This paper introduces a new class of odd-dimensional complex manifolds with Hodge structures similar to Calabi-Yau threefolds, providing new examples from rational homogeneous spaces.

Contribution

It defines and explores a novel class of manifolds with Calabi-Yau-like Hodge structures, including explicit constructions from rational homogeneous spaces.

Findings

Identified a new class of Calabi-Yau type manifolds.

Constructed several series of examples from rational homogeneous spaces.

Analyzed the Hodge structures of these manifolds.

Abstract

We introduce and we study a class of odd dimensional compact complex manifolds whose Hodge structure in middle dimension looks like that of a Calabi-Yau threefold. We construct several series of interesting examples from rational homogeneous spaces with special properties.