arXiv research

We obtain asymptotics of sequences of the holomorphic sections of the pluricanonical bundles on ball quotients associated to closed geodesics. A nonvanishing result follows.

A locally conformally Kahler manifold is a Hermitian manifold $(M,I,ω)$ satisfying $dω=θ\wedge ω$, where $θ$ is a closed 1-form, called the Lee form of $M$. It is called pluricanonical if $\nablaθ$ is of Hodge type $(2,0)+(0,2)$, where $\nabla$ is the Levi-Civita connection, and Vaisman if $\nablaθ=0$. We show that a c…

In this paper, we give some estimates of the sum of the square norm of the sections of the pluricanonical bundles over a Riemann surface with genus greater than 2 and Gauss curvature (-1). Using these estimate, we give a uniform estimate of the corona problem on Riemann surfaces.

Linear invariants of complex manifolds preserved by biholomorphisms.

We give a short proof of the fact that compact pluricanonical locally conformally Kähler manifolds have parallel Lee form.

The paper studies LCAK metrics on complex manifolds and their properties.

Extends BCOV invariant to pairs of Calabi-Yau manifolds and pluricanonical divisors.

Let $M$ be a regular Riemann surface with a metric which has constant scalar curvature $ρ$. We give the asymptotic expansion of the sum of the square norm of the sections of the pluricanonical bundles $K_{M}^{m}$. That is, \[\sum_{i=0}^{d_{m}-1}\|S_{i}(x_{0})\|_{h_{m}}^{2} \sim m(1+\fracρ{2 m})+O(e^{-\frac{(\log m)^{2}…

We treat two quite different problems related to changes of complex structures on Kähler manifolds by using global geometric method. First, by using operators from Hodge theory on compact Kähler manifold, we present a closed explicit extension formula for holomorphic canonical forms in different complex structures. As …

We propose a statistical mechanical derivation of Kahler-Einstein metrics, i.e. solutions to Einstein's vacuum field equations in Euclidean signature (with a cosmological constant) on a compact Kahler manifold X. The microscopic theory is given by a canonical free fermion gas on X whose one-particle states are plurican…

We provide examples of families of (log) smooth canonically polarized varieties, including smooth weighted pointed curves and smooth hypersurfaces in $P^3$ with large degree such that the Chow semistable limits under distinct pluricanonical embeddings do not stabilize.

Locally conformally Kahler (LCK) manifolds with potential are those which admit a Kahler covering with a proper, automorphic Kaehler potential. Existence of a potential can be characterized cohomologically as a vanishing of a certain cohomology class, called the Bott-Chern class. Compact LCK manifolds with potential ar…

We study the scalar curvature of Kähler metrics that have cone singularities along a divisor, with a particular focus on certain specific classes of such metrics that enjoy some curvature estimates. Our main result is that, on the projective completion of a pluricanonical bundle over a product of Kähler--Einstein Fano …

The paper proves a conjecture for Kähler fibre spaces.

This article is an attempt to generalize Riemann's bilinear relations on compact Riemann surface of genus at least 2, which may lead to new structures in the theory of hyperbolic Riemann surfaces. No significant result is obtained, the article serves to bring the readers' attention to the observation made by [Bol-1949]…

Study Kodaira dimensions on almost complex manifolds, proving integrability and structural descriptions.

We study one parameter degenerations of complex projective manifolds by introducing certain type of Hodge metrics coming from the pluricanonical forms. We show that degenerations with at most canonical singularities are all in the finite distance boundary of moduli spaces. We also propose the converse to be true in the…

A classical set of birational invariants of a variety are its spaces of pluricanonical forms and some of their canonically defined subspaces. Each of these vector spaces admits a typical metric structure which is also birationally invariant. These vector spaces so metrized will be referred to as the pseudonormed spaces…

The Kähler-Ricci flow yields bounded diameter and Ricci curvature for minimal models.

The Chern sectional curvature of a Hermitian manifold is derived and related to Kähler metrics.

Study Higgs sections and flat sections for nonlinear harmonic bundles.

Defines basic sections of LA-groupoids for simpler modeling.

This thesis predicts the distribution of smoothed zeros of random sections on line bundles.

New proof shows holomorphic sectional curvature fully determines curvature tensor.

Introduces homotopy momentum sections on multisymplectic manifolds.

Let $P(M,G)$ be a principal fiber bundle and $E(M,N,G,P)$ be an associate fiber bundle. Our interested is to study harmonic sections of the projection $π_{E}$ of $E$ into $M$. Our first purpose is to give a stochastic characterization of harmonic section from $M$ into $E$ and a geometric characterization of harmonic se…

Classifies surfaces of section for Seifert fibrations.

Study compact Kähler manifolds with nonpositive holomorphic sectional curvature and their canonical bundles.

Some optimization problems coming from the Differential Geometry, as for example, the minimal submanifolds problem and the harmonic maps problem are solved here via interior solutions of appropriate multitime optimal control problems. Section 1 underlines some science domains where appear multitime optimal control prob…

New method constructs Birkhoff sections for pseudo-Anosov flows with controlled complexity.

The paper proves that Kähler manifolds with positive holomorphic sectional curvature have a limited diameter.

The paper explores conditions for sections in Lefschetz fibrations and bundles over 2-complexes.

Study shows normal distribution in divisor counts of random sections on complex manifolds.

We prove the following results: An almost Hermitian manifold of indefinite metric is of pointwise constant holomorphic sectional curvature if the holomorphic sectional curvature is bounded from above and from below. If the antiholomorphic sectional curvature is bounded either from above or from below, then the manifold…

Introduces comomentum sections and proves they are Poisson maps.

It is proved that if an AK2-manifold of dimension greater or equal to 6 is of pointwise constant antiholomorphic sectional curvature, then it is a 6-dimensional manifold of constant negative sectional curvature or a Kähler manifold of constant holomorphic sectional curvature.

Formula for sectional curvature on 2D Lorentzian manifolds derived.

The φ-sectional curvature of statistical structures on almost contact metric manifolds is always non-positive.

Study calculates global sections on complex curves.

The study shows that symplectic Lefschetz fibrations can have infinitely many sections.

New maps show some surfaces can't be sections of 4D spheres.

The study examines when a section exists for graph configuration spaces.

We prove that a product complex manifold cannot admit a complete Kähler metric with sectional curvature $K<c<0$ and Ricci curvature $Ric > d$, where $c$ and $d$ are constants. In particular, a product domain in $\C$ cannot cover a compact Kähler manifold with negative sectional curvature. On the other hand, we observe …

The paper generalizes spectral section concepts to non-compact spaces.

Proves section conjecture for curves and surface bundles over various fields.

Generalizes momentum sections to higher-dimensional gauged sigma models.

The study extends cobordism theory to complex sections, defining and calculating cobordism groups.

The paper extends a theorem about Kähler manifolds with quasi-negative curvature to almost quasi-negative curvature.