Related papers: On the obstructions of deforming vector forms

The aim of this paper is to classify compact, simply connected K\"ahler manifolds which admit totally geodesic, holomorphic complex homothetic foliation by curves.

Twistor forms are a natural generalization of conformal vector fields on Riemannian manifolds. They are defined as sections in the kernel of a conformally invariant first order differential operator. We study twistor forms on compact…

To every morphism $\chi\colon L\to M$ of differential graded Lie algebras we associate a functors of artin rings $\Def_\chi$ whose tangent and obstruction spaces are respectively the first and second cohomology group of the cylinder of…

The work of Oh and Park ([OP]) on the deformation problem of coisotropic submanifolds opened the possibility of studying a large and interesting class of foliations with some explicit geometric tools. These tools assemble into the structure…

Using Quillen-Lurie deformation theory formalism we develop an obstruction theory for studying the stable $\infty$-category of modules over a given geometric $\infty$-stack. The obstruction theory studies the problem of lifting compact…

We introduce a variant of the usual Kahler forms on free and almost free divisors and their deformations, and show that they enjoy the same depth properties as Kahler forms on isolated complete intersection singularities. Using these forms,…

We give an elementary proof of the result by Leichtnam, Tang, and Weinstein that there exists a deformation quantization with separation of variables on a complex manifold endowed with a Kaehler-Poisson structure vanishing on a Levi…

A classification theorem for nearly K\"ahler manifolds of constant antiholomorphic sectional curvature is proved.

We give an answer to the Nielsen realization problem for hyper-K\"ahler manifolds in terms of the same invariant used for K3 surfaces. We determine that, for some of the known deformation types, the representation of the mapping class group…

We show that the Hochschild cohomology of the algebra obtained by formal deformation quantization on a symplectic manifold is isomorphic to the formal series with coefficients in the de Rham cohomology of the manifold. The cohomology class…

We calculate relations on characteristic classes which are obstructions preventing closed K\"ahler manifolds from carrying holomorphic Cartan geometries. We apply these relations to give global constraints on the phase spaces of complex…

In this paper we address the following question: is it always possible to choose a deformation quantization of a Poisson algebra A so that certain Poisson-commutative subalgebra C in it remains commutative? We define a series of…

Nonvanishing theorems play a central role in birational geometry, since they derive geometric consequences from numerical information and constitute a crucial step towards abundance and semiampleness problems. General nonvanishing…

We give a bimeromorphic classification of compact K\"ahler manifolds of Kodaira codimension one that admit a holomorphic one form without zeros.

We show that the first twisted cohomology group associated to closed 1-forms on compact manifolds is related to certain 2-dimensional representations of the fundamental group. In particular, we construct examples of nowhere-vanishing…

We consider 6-dimensional strict nearly Kaehler manifolds acted on by a compact, cohomogeneity one automorphism group G. We classify the compact manifolds of this class up to G-diffeomorphisms. We also prove that the manifold has constant…

In this work, we study Monge-Ampere equations over closed K\"ahler manifolds with degenerated cohomology classes. Classic results and arguments in pluripotential theory are generalized a little bit to be applied to our situation.

It has been shown by Claire Voisin in 2003 that one cannot always deform a compact K\"ahler manifold into a projective algebraic manifold, thereby answering negatively a question raised by Kodaira. In this article, we prove that under an…

A complete description of the deformation classes of real ruled manifolds is given. In particular, we prove that once the complex deformation class is fixed, the real deformation class is prescribed by the topology of the real structure.

In this thesis, we study cohomological properties of non-K\"ahler manifolds. In particular, we are concerned in investigating the cohomology of compact (almost-)complex manifolds, and of manifolds endowed with special structures, e.g.,…