Branes on Poisson varieties

TL;DR

This paper introduces new characterizations of generalized Kaehler geometry via Courant algebroid connections, proposes a novel non-holomorphic isomorphism for holomorphic Poisson manifolds, and constructs new generalized Kaehler structures on compact Poisson manifolds, linking branes and non-commutative geometry.

Contribution

It extends the notion of connections in Courant algebroids, defines a non-holomorphic isomorphism for Poisson manifolds, and constructs new generalized Kaehler structures on compact holomorphic Poisson manifolds.

Findings

New characterization of generalized Kaehler geometry

A novel non-holomorphic isomorphism between Poisson manifolds

Explicit construction of generalized Kaehler structures on Fano manifolds

Abstract

We first extend the notion of connection in the context of Courant algebroids to obtain a new characterization of generalized Kaehler geometry. We then establish a new notion of isomorphism between holomorphic Poisson manifolds, which is non-holomorphic in nature. Finally we show an equivalence between certain configurations of branes on Poisson varieties and generalized Kaehler structures, and use this to construct explicitly new families of generalized Kaehler structures on compact holomorphic Poisson manifolds equipped with positive Poisson line bundles (e.g. Fano manifolds). We end with some speculations concerning the connection to non-commutative algebraic geometry.