Bihermitian metrics on Del Pezzo surfaces

TL;DR

This paper introduces a method to construct a family of bihermitian metrics on Del Pezzo surfaces using hermitian metrics and holomorphic sections, revealing potential links to noncommutative geometry.

Contribution

It presents a novel construction of bihermitian metrics on Del Pezzo surfaces from hermitian metrics and sections, connecting complex geometry with noncommutative geometry.

Findings

Constructs a one-parameter family of bihermitian metrics

Establishes a link between hermitian metrics and generalized Kähler structures

Suggests connections to noncommutative geometry

Abstract

From a hermitian metric on the anticanonical bundle on a Del Pezzo surface, and a holomorphic section of it, we construct a one parameter family of bihermitian metrics (or equivalently generalized Kaehler structures). The construction appears to be linked to noncommutative geometry.