Related papers: Remarks on the extension of twisted Hodge metrics

In this survey, we review recent developments in extending Hodge theory to differential forms with values in bundles equipped with singular metrics, based on joint work with Ya Deng, Christopher D. Hacon, and Mihai P\u{a}un.

A systematic study of the contributions at infinity for the cohomology of variations of polarized Hodge structures over quasicompact K\"ahler manifolds. Several isomorphisms between different cohomologies given.

These are notes on twisted K-homology theory and twisted Ext-theory from the C*-algebra viewpoint, part of a series of talks on ``C*-algebras, noncommutative geometry and K-theory'', primarily for physicists.

Let f : X --> Y be a holomorphic map of complex manifolds, which is proper, Kahler, and surjective with connected fibers, and which is smooth over Y-Z the complement of an analytic subset Z. Let E be a Nakano semi-positive vector bundle on…

An exposition of the basic geometry of twistor integrals, intended for mathematicians.

We prove an existence result for twisted K\"ahler-Einstein metrics, assuming an appropriate twisted K-stability condition. An improvement over earlier results is that certain non-negative twisting forms are allowed.

This paper extends our earlier results to higher dimensions using a different approach, based on the rigidity of complex structures on certain domains.

This is a survey article, based on the author's lectures in the 2015 Current developments in Mathematics meeting; published in "Current developments in Mathematics". Version 2, references corrected and added.

We construct a braided structure on the algebra of K\"ahler differential forms of a commutative algebra twisted by an endomorphism. This generalises the construction done in M. Karoubi, Quantum Methods in Algebraic Topology, see…

We survey some recent results and constructions of almost-K\"ahler manifolds whose curvature tensors have certain algebraic symmetries. This is an updated and corrected version of the (to be) published manuscript.

We investigate properties of the Hodge metric of a mixed period domain. In particular, we calculate its curvature and the curvature of the Hodge bundles. We also consider when the pull back metric via a period map is K\"ahler. Several…

In this paper, we extend the Burghelea-Haller analytic torsion to the twisted de Rham complexes. We also compare it with the twisted refined analytic torsion defined by Huang.

We discuss twisted cohomology, not just for ordinary cohomology but also for $K$-theory and other exceptional cohomology theories, and discuss several of the applications of these in mathematical physics. Our list of applications is by no…

This text is an expository survey on the interplay between polarized variation of Hodge structure (PVHS) and the formalism of Hodge modules. We specifically review the extensions of a PVMHS over their singularities and its relation to mixed…

We introduce new concepts in order to develop a general formalism for twisted differential operators in several variables. We investigate the notion of twisted coordinates on Huber rings that allows us to build various rings of twisted…

We show that our earlier work in \cite{LT05} extends to the twisted case, that is, we defined a notion of moment map and reduction in both twisted generalized complex geometry and twisted generalized K\"ahler geometry.

I give a short review of the theory of twisted symmetries of differential equations, emphasizing geometrical aspects. Some open problems are also mentioned.

We point out how some recent developments in the theory of constant scalar curvature K\"ahler metrics can be used to clarify the existence issue for such metrics in the special case of geometrically ruled complex surfaces.

The aim of this work is to give a twistor presentation of recent results about bi-Hermitian metrics on compact complex surfaces with odd first Betti number.

The purpose of this paper is to study hom-algebroids, among them left symmetric hom-algebroids and symplectic hom-algebroids by providing some characterizations and geometric interpretations. Therefore, we introduce and study…