arXiv research

Formula for analytic torsion forms in fibrations by projective curves.

Study fibrations of projective spaces for maximal representations.

Researchers create a projective space for quasimaps and study its connections to Calabi-Yau fibrations.

Classifies surfaces of section for Seifert fibrations.

We develop some theory of double fibration transforms where the cycle space is a smooth manifold and apply it to complex projective space.

In this paper, we study asymptotic behavior of projective embeddings of Kummer varieties given by theta functions, and their amoebas. We prove that a Lagrangian fibration of the Kummer variety can be approximated by moment maps of the projective spaces.

Study shows special Kähler geometry on base of holomorphic Lagrangian fibrations implies projective space.

Classifies foliations of complex and quaternionic projective spaces.

The paper studies algebraic fibre spaces with specific properties and proves key results about their structure.

Study nondegenerate fibrations of Euclidean spaces and their relation to sphere fibrations.

Let X be a compact hyperkähler manifold containing a complex torus L as a Lagrangian subvariety. Beauville posed the question whether X admits a Lagrangian fibration with fibre L. We show that this is indeed the case if X is not projective. If X is projective we find an almost holomorphic Lagrangian fibration with fibr…

Banach fibrations and Nijenhuis operators studied for vanishing torsion.

Let $\mathcal{G} \rightrightarrows M$ be a source locally trivial proper Lie groupoid such that each orbit is of finite type. The orbit projection $M \to M/\mathcal{G}$ is a fibration if and only if $\mathcal{G} \rightrightarrows M$ is regular.

In this paper, we consider a special relative Kähler fibration that satisfies a homogenous Monge-Ampère equation, which is called a Monge-Ampère fibration. There exist two canonical types of generalized Weil-Petersson metrics on the base complex manifold of the fibration. For the second generalized Weil-Petersson metri…

The main goal of this work is to study the sub-Laplacian of the unit sphere which is obtained by lifting with respect to the Hopf fibration the Laplacian of the quaternionic projective space. We obtain in particular explicit formulas for its heat kernel and deduce an expression for the Green function of the conformal s…

We study finite-time collapsing limits of the continuity method. When the continuity method starting from a rational initial Kähler metric on a projective manifold encounters a finite-time volume collapsing, this projective manifold admits a Fano fibration over a lower dimensional base. In this case, we prove the conti…

Synthetic construction of Hopf fibration in 4D space.

Introduces Hurewicz fibrations for embedding maps of orbifold charts.

The paper studies deformations of Lagrangian fibrations on symplectic manifolds.

In this paper we study two types of fibrations associated with a 3-dimensional unital associative irreducible algebra and their basic properties. We investigate trivial principal fibrations of degenerate semi-Euclidean sphere and their semi-conformal and projective models. We use Norden normalization method for constru…

In this thesis we study asymptotic behavior of projective embeddings of abelian varieties and their amoebas. The projective embeddings are given by theta functions. It is known that a Lagrangian fibration of the abelian variety determines a basis of theta functions. After reviewing the relation from the viewpoint of ge…

The notion of generalized Seifert fibration is introduced, it is shown that the projections of certain Eschenburg $7$-manifolds onto ${\mathbb C} P^2$ define such fibrations, and for them the characteristic classes corresponding to the generators of $H^2(B(U(2)/{\mathbb Z}_{2n});{\mathbb Z})$ are defined.

It is known that an arbitrary smooth, oriented 4-manifold admits the structure of what is called a broken Lefschetz fibration. Given a broken fibration, there are certain modifications, realized as homotopies of the fibration map, that enable one to construct infinitely many distinct fibrations of the same manifold. Th…

The study of projective varieties with nef anticanonical divisors and log terminal singularities.

The paper extends structure theorem to projective klt varieties with specific tangent sheaf properties.

The orbit projection $π: M \to M/G$ of a proper $G$-manifold $M$ is a fibration if and only if all points in $M$ are regular. Under additional assumptions we show that $π$ is a quasifibration if and only if all points are regular. We get a full answer in the equivariant category: $π$ is a $G$-quasifibration if and only…

In this paper, we pose several conjectures on structures and images of maximal rationally connected fibrations of smooth projective varieties admitting semi-positive holomorphic sectional curvature. Toward these conjectures, we prove that the canonical bundle of images of such fibrations is not big. Our proof gives a g…

Extends Serre-Swan theorem to all finitely generated modules over smooth functions.

This paper classifies fibrations of flat orbifolds, advancing flat 4-manifold classification.

The abstract proves a Moser-like theorem for C-symplectic structures and applies it to complex manifolds.

Study of Calabi-Yau metrics on converging manifolds, resolving conjectures.

For every fibration $f : X \to B$ with $X$ a compact Kähler manifold, $B$ a smooth projective curve, and a general fiber of $f$ an abelian variety, we prove that $f$ has an algebraic approximation.

In the paper we introduce the notions of a singular fibration and a singular Seifert fibration. These notions are natural generalizations of the notion of a locally trivial fibration to the category of stratified pseudomanifolds. For singular foliations defined by such fibrations we prove a de Rham type theorem for the…

The paper shows that certain geometric structures remain unchanged under specific twists.

The Hopf fibration has inspired any number of geometric structures in physical systems, in particular in chiral liquid crystalline materials. Because the Hopf fibration lives on the three sphere, $\mathbb{S}^3$, some method of projection or distortion must be employed to realize textures in flat space. Here, we explore…

Constructs families of Toeplitz operators for symplectic fibrations.

We establish a product formula for Gromov-Witten invariants for closed, connected, relatively semi-positive Hamiltonian fibrations over any symplectic base. Furthermore, we show that the fibration projection induces a locally trivial (orbi-)fibration map from the moduli space of pseudo-holomorphic maps with marked poin…

Solves open problems on curved projective varieties.

New symplectic caps and embeddings found in complex projective plane.

A complex projective tower or simply a $\mathbb CP$-tower is an iterated complex projective fibrations starting from a point. In this paper we classify all 6-dimensional $\mathbb CP$-towers up to diffeomorphism, and as a consequence, we show that all such manifolds are cohomologically rigid, i.e., they are completely d…

We review how a reduction procedure along a principal fibration and an unfolding procedure associated to a suitable momentum map allow to describe the Kähler geometry of a finite dimensional complex projective spaces.

We give a criterion for a projective surface to become a quotient of a fake projective plane. We also give a detailed information on the elliptic fibration of a $(2,3)$-elliptic surface that is the minimal resolution of a quotient of a fake projective plane. As a consequence, we give a classification of ${\mathbb Q}$-h…

Study $π$-equigeodesic vectors in homogeneous fibrations.

We are going to use the Euler's vector fields in order to show that for real quasi-homogeneous singularities with isolated critical value, the Milnor's fibration in a "thin" hollowed tube involving the zero level and the fibration in the complement of "link" in sphere are equivalents, since they exist. Moreover, in ord…

Non-archimedean SYZ fibration constructed for Calabi-Yau hypersurfaces.

The paper connects Kähler-Ricci shrinkers to Fano fibrations in algebraic geometry.

Study connects surface projections in fibered 3-manifolds.

Researchers classify geodesic orbit spaces for compact Lie groups of rank two.