Related papers: Some remarks on fibrations in complex geometry
A holomorphic Lagrangian fibration on a holomorphically symplectic manifold is a holomorphic map with Lagrangian fibers. It is known that a given compact manifold admits only finitely many holomorphic symplectic structures, up to…
We suggest a general framework for compactifing quasi-projective Lagrangian fibrations of geometric origin by holomorphic symplectic varieties. This framework includes a compactification criterion, which we then apply to various fibrations…
We compute the Hodge filtration on cohomology groups of complements of complex coordinate subspace arrangements. By means of this result we construct integral representations of holomorphic functions such that kernels of these…
We study the integrability of a (almost) complex structure calibrated by a symplectic form. We find new sufficent conditions.
This paper is devoted to a discussion of specific properties of invariants in the theory of forms.
In this article, we study various concrete algebraic and differential geometric properties of the Cartwright-Steger surface. In particular, we determine the genus of a generic fiber of the Albanese fibration, and deduce that the singular…
In order to study the problems of extending an action along a quotient of the acted object and along a quotient of the acting object, we investigate some properties of the fibration of points. In fact, we obtain a characterization of…
We develop a real-analytic framework, called perplex analysis, in which the complex, split-complex, and dual numbers arise as members of a single four-parameter family of two-dimensional commutative real algebras. Within this unified…
Let $C$ be a smooth elliptic curve embedded in a smooth complex surface $X$ such that $C$ is a leaf of a suitable holomorphic foliation of $X$. We investigate complex analytic properties of a neighborhood of $C$ under some assumptions on…
The paper is devoted to introduce some notions extending the unique path lifting property from a homotopy viewpoint and to study their roles in the category of fibrations. First, we define some homotopical kinds of the unique path lifting…
This is an expository paper which presents the holomorphic classification of rational complex surfaces from a simple and intuitive point of view, which is not found in the literature. Our approach is to compare this classification with the…
The novel concept of box spline of complex degree is introduced and several of its properties derived and discussed. These box splines of complex degree generalize and extend the classical box splines. Relations to a class of fractional…
We study constructions of contact forms on closed manifolds. A notion of strong symplectic fold structure is defined and we prove that there is a contact form on $M \x X$ provided that $M$ admits such a structure and $X$ is contact. This…
A Kodaira fibration is a compact, complex surface admitting a holomorphic submersion onto a complex curve, such that the fibers have nonconstant moduli. We consider Kodaira fibrations X with nontrivial invariant rational cohomology in…
We investigate the geometry of holomorphic curves and complex surfaces from the perspective of singularity theory. We show that, with a suitable choice of a complex bilinear symmetric form, the families of functions and mappings that…
Several characterizations of complex ellipsoids among convex bodies in Cn, in terms of their sections and projections are proved. Characterizing complex symmetry in similar terms is an important tool.
The class of the hypercomplex pseudo-Hermitian manifolds is considered. The flatness of the considered manifolds with the 3 parallel complex structures is proved. Conformal transformations of the metrics are introduced. The conformal…
We study generalized complex cohomologies of generalized complex structures constructed from certain symplectic fibre bundles over complex manifolds. We apply our results in the case of left-invariant generalized complex structures on…
In this article, we study and review some aspects of twisted cohomologies on algebraic and analytic varieties. We compared such cohomologies in both the algebraic and analytic categories and defined two types of twisting parameters in the…
In this paper we find all complex symmetric weighted composition operators with special conjugations. Then we give spectral properties of these complex symmetric weighted composition operators.