Gibson, Matthew Streets, Jeffrey
Published in
Complex Manifolds

We describe natural deformation classes of generalized Kähler structures using the Courant symmetry group, which determine natural extensions of the notions of Kähler class and Kähler cone to generalized Kähler geometry. We show that the generalized Kähler-Ricci flow preserves this generalized Kähler cone, and the underlying real Poisson tensor.

Ballico, Edoardo Huh, Sukmoon
Published in
Mediterranean Journal of Mathematics

In this article, we introduce a notion of logarithmic co-Higgs sheaves associated with a simple normal crossing divisor on a projective manifold and show their existence with nilpotent co-Higgs fields for fixed ranks and second Chern classes. Then, we deal with various moduli problems involving logarithmic co-Higgs sheaves, such as coherent systems...

Nannicini, Antonella
Published in
Bollettino dell'Unione Matematica Italiana

We study extensions of Norden structures on manifolds to their generalized tangent bundles and to their cotangent bundles. In particular, by using methods of generalized geometry, we prove that the cotangent bundle of a complex Norden manifold (M, J, g) admits a structure of Norden manifold, (T⋆(M),J~,g~)\documentclass[12pt]{minimal} \usepackage{am...

Katzarkov, Ludmil Soriani, Leonardo
Published in
European Journal of Mathematics

We discuss the P=W\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P=W$$\end{document} conjecture and suggest and a new approach to it using the theory of coisotropic br...

Davidov, Johann
Published in
Mathematische Zeitschrift

The twistor construction for Riemannian manifolds is extended to the case of manifolds endowed with generalized metrics (in the sense of generalized geometry à la Hitchin). The generalized twistor space associated to such a manifold is defined as the bundle of generalized complex structures on the tangent spaces of the manifold compatible with the ...

Ballico, Edoardo Huh, Sukmoon
Published in
manuscripta mathematica

A co-Higgs sheaf on a smooth complex projective variety X is a pair of a torsion-free coherent sheaf E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {E}$$\end...

Garcia-Fernandez, Mario Rubio, Roberto Tipler, Carl
Published in
Mathematische Annalen

We construct the space of infinitesimal variations for the Strominger system and an obstruction space to integrability, using elliptic operator theory. We initiate the study of the geometry of the moduli space, describing the infinitesimal structure of a natural foliation on this space. The associated leaves are related to generalized geometry and ...

Ida, Cristian Manea, Adelina
Published in
Mediterranean Journal of Mathematics

In this paper, we investigate the ∇\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nabla $$\end{document} integrability of generalized almost para-Norden/para-Hermitia...

Liu, Jiefeng Sheng, Yunhe Bai, Chengming
Published in
Letters in Mathematical Physics

In this paper, we introduce the notion of a pre-symplectic algebroid and show that there is a one-to-one correspondence between pre-symplectic algebroids and symplectic Lie algebroids. This result is the geometric generalization of the relation between left-symmetric algebras and symplectic (Frobenius) Lie algebras. Although pre-symplectic algebroi...

Ševera, Pavol Valach, Fridrich
Published in
Letters in Mathematical Physics

We use a generalized Ricci tensor, defined for generalized metrics in Courant algebroids, to show that Poisson–Lie T-duality is compatible with the 1-loop renormalization group flow.