arXiv research

Introduces new stability concept for Fano fibrations.

Complete Calabi-Yau metrics on abelian fibrations over complex space.

New homogeneous representations of contact metric spaces identified.

We explore a number of examples of special Lagrangian fibrations on non-compact Calabi-Yau manifolds invariant under torus actions. These include fibrations on crepant resolutions of canonical toric singularities (already found by Goldstein), proper versions of these fibrations, and fibrations on flat deformations of c…

The paper proves properties of image structures of fibrations with semi-positive curvature.

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

The paper proves conditions for minimal compact Kähler manifolds with vanishing second Chern class.

Study shows scalar curvature of a specific type of manifold converges to -m outside singular points.

We construct a positive allowable Lefschetz fibration over the disk on any minimal weak symplectic filling of the canonical contact structure on a lens space. Using this construction we prove that any minimal symplectic filling of the canonical contact structure on a lens space is obtained by a sequence of rational blo…

The Kähler-Ricci flow on certain manifolds collapses to a canonical metric.

In this note we show that if a compact Kahler manifold with trivial canonical bundle is the total space of a holomorphic fibration without singular fibers, then the fibration is a holomorphic fiber bundle. In the algebraic case, the fibration becomes trivial after a finite base change.

Uniform diameter bounds for Calabi-Yau fibrations with singular fibers.

The paper finds Kähler-Einstein metrics on certain degenerations.

A genus one Lefschetz fibration is described for disk cotangent bundles of surfaces.

Study para-Sasakian φ-symmetric spaces using Boothby-Wang fibration.

Study projective klt pairs with nef anti-canonical divisor and their properties.

Banach fibrations and Nijenhuis operators studied for vanishing torsion.

Given a (meromorphic) fibration $f:X\to Y$ where $X$ and $Y$ are compact complex manifolds of dimensions $n$ and $m$, we define $L_f$ to be the invertible subsheaf of the sheaf of holomorphic $m$-forms of $X$ given by the saturation of $f^*K_Y$, where $K_Y$ is the canonical sheaf of $Y$. We define the Kodaira dimension…

Canonical twistor fibrations lead to Pfaffian systems by means of their superhorizontal distribution. The aim of this note is to identify explicitly the Pfaffian systems of five or less variables that arise in this way in terms of the classification given by A.Awane and M.Goze.

Two remarks on curvature properties of Kähler manifolds.

We describe a simple way of constructing torus fibrations $T^3\to X\to S^3$ which degenerate canonically over a knot or link in $S^3$. We show that the topological invariants of $X$ can be computed algebraically from the monodromy representation of the fibration. We use this to obtain some new $T^3$-fibrations $S^3\tim…

The article describes canonical metrics on holomorphic fibre bundles.

Study Moishezon twistor spaces using quartic hypersurfaces and Del Pezzo fibrations.

Clarifies relation between Pfaffian fibrations and relative algebroids.

In the first part of this paper we consider compact algebraic manifolds M^2n with an algebraic (n-1)-Torus action. We show that there is a T-invariant meromorphic section $σ$ of the canonical bundle of M. Any such $σ$ defines a divisor D. On the complement M'=M-D we have a trivialization of the canonical bundle and a T…

The paper shows how compact Kähler manifolds with a special bundle can be broken down into simpler parts.

In this paper, we study hyperkahler metric and practice GMN's construction of hyperkahler metric on focus-focus fibrations. We explicitly compute the action-angel coordinates on the local model of focus-focus fibration, and show its semi-global invariant should be harmonic to admit a compatible holomorphic 2-form. Then…

Unbraided wiring diagrams for Stein fillings of lens spaces are described.

The usual formulation of time-dependent mechanics implies a given splitting $Y=R\times M$ of an event space $Y$. This splitting, however, is broken by any time-dependent transformation, including transformations between inertial frames. The goal is the frame-covariant formulation of time-dependent mechanics on a bundle…

New solutions found for complex structures on specific manifolds.

Quantizes symplectic fibrations to analyze vector bundles and metrics.

We consider a class of compact homogeneous CR manifolds, that we call $\mathfrak n$-reductive, which includes the orbits of minimal dimension of a compact Lie group $K_0$ in an algebraic homogeneous variety of its complexification $K$. For these manifolds we define canonical equivariant fibrations onto complex flag man…

The paper studies curvature properties of Monge-Ampère fibrations and their existence.

Study on Kähler-Ricci flow's infinite-time singularities.

Constructs a new type of metric for elliptic surfaces.

The paper connects moment maps to the stability of holomorphic fibrations.

In this paper we classify symplectic Lefschetz fibrations (with empty base locus) on a four-manifold which is the product of a three-manifold with a circle. This result provides further evidence in support of the following conjecture regarding symplectic structures on such a four-manifold: if the product of a three-man…

We describe a new approach to the canonical decompositions of 3-manifolds along tori and annuli due to Jaco-Shalen and Johannson (with ideas from Waldhausen) - the so-called JSJ-decomposition theorem. This approach gives an accessible proof of the decomposition theorem; in particular it does not use the annulus-torus t…

Reviews interactions between Spin(9) and octonionic geometries.

Study Fano fibrations and Kähler-Einstein metrics on their bases.

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

We present explicit constructions of complete Ricci-flat Kahler metrics that are asymptotic to cones over non-regular Sasaki-Einstein manifolds. The metrics are constructed from a complete Kahler-Einstein manifold (V,g_V) of positive Ricci curvature and admit a Hamiltonian two-form of order two. We obtain Ricci-flat Ka…

We consider the family of constant curvature fiber metrics for a Lefschetz fibration with regular fibers of genus greater than one. A result of Obitsu and Wolpert is refined by showing that on an appropriate resolution of the total space, constructed by iterated blow-up, this family is log-smooth, i.e. polyhomogeneous …

We consider canonical fibrations and algebraic geometric structures on homogeneous CR manifolds, in connection with the notion of CR algebra. We give applications to the classifications of left invariant CR structures on semisimple Lie groups and of CR-symmetric structures on complete flag varieties.

Authors compute monodromy groups for SL(n) and GL(n) Hitchin fibrations.

For integrable Hamiltonian systems with two degrees of freedom whose Hamiltonian vector fields have incomplete flows, an analogue of the Liouville theorem is established. A canonical Liouville fibration is defined by means of an "exact" 2-parameter family of flat polygons equipped with certain pairing of sides. For the…

We describe a family of locally conformal Kaehler metrics on class 1 Hopf surfaces H containing some recent metrics constructed by P. Gauduchon and L. ornea. We study some canonical foliations associated to these metrics, in particular a 2-dimensional foliation E that is shown to be independent of the metric. We elemen…

Introduces stability for families of K-polystable varieties and connects it to optimal symplectic connections.