Related papers: Forms and Complex Manifolds

In this article, we study some properties of deformation invariance of the Gamma-dimension (defined for X a compact k\"ahler manifold). This birational invariant is defined as the codimension of the maximal compact subvarieties in the…

A hyperk\"ahler manifold is defined as a Riemannian manifold endowed with three covariantly constant complex structures that are quaternionically related. A twistor space is characterized as a holomorphic fiber bundle $p: \mathcal{Z}…

We show that if a compact Kahler manifold X admits a cohomologically hyperbolic surjective endomorphism then its Kodaira dimension is non-positive. This gives an affirmative answer to a conjecture of Guedj in the holomorphic case. The main…

We study the special algebraic properties of alternating 3-forms in 6 and 7 dimensions and introduce a diffeomorphism-invariant functional on the space of differential 3-forms on a closed manifold M in these dimensions. Restricting the…

Let $X$ be a compact, oriented, second countable pseudomanifold. We show that $HH^\ast_\bullet(\widetilde N^\ast_\bullet(X;\mathbb{Q}))$, the Hochschild cohomology of the blown-up intersection cochain complex of $X$, is well defined and…

We study geometry, topology and deformation spaces of noncompact complex hyperbolic manifolds (geometrically finite, with variable negative curvature), whose properties make them surprisingly different from real hyperbolic manifolds with…

We investigate complex structures on the Oeljeklaus-Toma manifolds. The Oeljeklaus-Toma manifolds are defined using complex embeddings of number fields. By replacing these embeddings with their conjugates, one obtains other manifolds that…

We study the J-invariant and J-anti-invariant cohomological subgroups of the de Rham cohomology of a compact manifold M endowed with an almost-K\"ahler structure (J, \omega, g). In particular, almost-K\"ahler manifolds satisfying a…

The properties of Kaehler submanifolds with recurrent the second fundamental form in spaces of constant holomorphic sectional curvature are being studied in this article.

We shall show how to decompose, by functorial and canonical fibrations, arbitrary $n$-dimensional complex projective {Although the geometric results apply to compact K\" ahler manifolds without change, we consider here for simplicity this…

We study holomorphic foliations of codimension $k\geq 1$ on a complex manifold $X$ of dimension $n+k$ from the point of view of the exceptional minimal set conjecture. For $n\geq 2$ we show in particular that if the holomorphic normal…

In this paper, we investigate the two-dimensional complex Finsler manifolds. The tools of this study are the complex Berwald frames and the Chern-Finsler connection with respect to these frames.

This is partly a survey and partly a research article. Some known results and open problems about Kaehler groups (fundamental groups of compact Kaehler manifolds) are discussed. A new notion of Kaehler homomorphism is introduced. This is a…

On a compact K\"{a}hler manifold $X$ with a holomorphic 2-form $\a$, there is an almost complex structure associated with $\a$. We show how this implies vanishing theorems for the Gromov-Witten invariants of $X$. This extends the approach,…

We study cohomological properties of complex manifolds. In particular, under suitable metric conditions, we extend to higher dimensions a result by A. Teleman, which provides an upper bound for the Bott-Chern cohomology in terms of Betti…

In this paper, we survey recent works on the structure of the mapping class groups of surfaces mainly from the point of view of topology. We then discuss several possible directions for future research. These include the relation between…

In this note, we survey our recent work concerning cohomologies of harmonic bundles on quasi-compact Kaehler manifolds.

We settle two problems of reconstructing a biholomorphic type of a manifold. In the first problem we use graphs associated to Riemann surfaces of a particular class. In the second one we use the semigroup structure of analytic endomorphisms…

In this paper, we study the complex structures of complete hyperk\"ahler four-manifolds of infinite topological type arising from the Gibbons-Hawking ansatz. We show that for almost all complex structures in the hyperk\"ahler family, the…

In this paper we analyse the birational geometry of O'Grady ten dimensional manifolds, giving a characterisation of Kaehler classes and lagrangian fibrations. Moreover, we study symplectic compactifications of intermediate jacobian…