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.
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...
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...
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...
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 ...
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...
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 ...
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...
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...
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.
