Related papers: Blowdowns and McKay correspondence on four dimensi…
Some ball-quotient orbifolds are related by covering maps. We exploit these coverings to find infinite towers of orbifolds uniformized by the complex 2-ball and some orbifolds over K3 surfaces uniformized by the 2-ball. Corresponding…
In this paper, we study the prescribed $Q$-curvature problem on closed four-dimensional Riemannian manifolds when the total integral of the $Q$-curvature is a positive integer multiple of the one of the four-dimensional round sphere. This…
The K-rings of non-singular complex pro jective varieties as well as quasi- toric manifolds were described in terms of generators and relations in an earlier work of the author with V. Uma. In this paper we obtain a similar description for…
We study the closure of a complex subtorus in a toric manifold. If the closure of the complex subtorus is a smooth complex submanifold in the toric manifold, then the subtorus action on such submanifold is Hamiltonian. In this case, we may…
Given a singular hypersurface in a regular 2-dimensional scheme essentially of finite type over a field, we construct an embedded resolution of singularities by weighted blow-ups. This differs from our earlier work which required…
The famous conjecture of V.Ya.Ivrii says that {\it in every billiard with infinitely-smooth boundary in a Euclidean space the set of periodic orbits has measure zero}. In the present paper we study its complex analytic version for…
The aim of this paper is to construct Calabi-Yau 4-folds as crepant resolutions of the quotients of a hyperk\"ahler 4-fold $X$ by a non symplectic involution $\alpha$. We first compute the Hodge numbers of a Calabi-Yau constructed in this…
We demonstrate the existence of quasiconformal mappings on closed manifolds that cannot be decomposed as a composition of mappings with arbitrarily small conformal distortion.
Let $M^n$, $n \in \{4,5,6\}$, be a compact, simply connected $n$-manifold which admits some Riemannian metric with non-negative curvature and an isometry group of maximal possible rank. Then any smooth, effective action on $M^n$ by a torus…
The Leit-Faden of the article (which is partially a survey) is a negative answer to the question whether, for a compact complex manifold which is a $K(\pi, 1)$ the diffeomorphism type determines the deformation type. We show that a…
A hypercomplex manifold is a manifold with three complex structures satisfying quaternionic relations. Such a manifold admits a unique torsion-free connection preserving the quaternionic action, called the Obata connection. A compact Kahler…
We study novel type of contributions to the entropy of the Maxwell system defined on a compact manifold such as torus. These new terms are not related to the physical propagating photons. Rather, these novel contributions emerge as a result…
Let $X$ be a complex four-dimensional compact Calabi-Yau manifold equipped with a K\"ahler form $\omega$ and a holomorphic four-form $\Omega$. Under certain assumptions, we define Donaldson-Thomas type deformation invariants by studying the…
The aim of this paper is to consider quasi-linear systems which are not in the form of evolution equations. We propose new condition of Richness or Semi-Hamiltonicity for such a system and prove that the blow up analysis along…
Four observations compose the main results of this note. The first records the existence of a smoothly embedded 2-sphere $S$ inside $\mathbb{R} P^2\times S^2$ such that performing a Gluck twist on $S$ produces a manifold $Y$ that is…
The CW structure of certain spaces, such as effective orbifolds, can be too complicated for computational purposes. In this paper we use the concept of $\mathbf{q}$-CW complex structure on an orbifold, to detect torsion in its integral…
We consider the problem of comparing t-structures under the derived McKay correspondence and for tilting equivalences. We relate the t-structures using certain natural torsion theories. As an application, we give a criterion for rationality…
In this note we prove that a four-dimensional compact oriented half-confor\-mally flat Riemannian manifold $M^4$ is topologically $\mathbb{S}^{4}$ or $\mathbb{C}\mathbb{P}^{2},$ provided that the sectional curvatures all lie in the interval…
We introduce a topological invariant, it a type of a graph-manifold, which takes natural values. For a 4-dimensional graph-manifold, whose type does not exceed two, it is proved that its universal cover is bi-Lipschitz equivalent to a…
This paper pursues the study of the Calabi-Yau equation on certain symplectic non-Kaehler 4-manifolds, building on a key example of Tosatti-Weinkove in which more general theory had proved less effective. Symplectic 4-manifolds admitting a…