arXiv research

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

Let $(X, D)$ be a logarithmic pair, and let $h$ be a singular metric on the tangent bundle, smooth on the open part of $X$. We give sufficient conditions on the curvature of $h$ for the logarithmic and the standard cotangent bundles to be big. As an application, we give a metric proof of the bigness of logarithmic cota…

Let $M$ and $N$ be two compact complex manifolds. We show that if the tautological line bundle $\mathscr{O}_{T_M^*}(1)$ is not pseudo-effective and $\mathscr{O}_{T_N^*}(1)$ is nef, then there is no non-constant holomorphic map from $M$ to $N$. In particular, we prove that any holomorphic map from a compact complex mani…

Explains differences and similarities of strictly nef and ample vector bundles.

Study projective KLT varieties with projectively flat cotangent sheaves.

Study positive characteristic Fano 4-folds with nef tangent bundles.

The paper proves inequalities for orbifold second Chern classes in Fujiki's class.

In this paper, we show that if the tangent bundle of a smooth projective variety is strictly nef, then it is isomorphic to a projective space; if a projective variety $X^n$ $(n>4)$ has strictly nef $Λ^2 TX$, then it is isomorphic to $\mathbb{P}^n$ or quadric $\mathbb{Q}^n$. We also prove that on elliptic curves, strict…

The paper proves structures for complex projective varieties with certain tangent bundle properties.

We prove that any Fano manifold of coindex three admitting nef tangent bundle is homogeneous.

In this paper we study holomorphic vector bundles with singular Hermitian metrics whose curvature are Hermitian matrix currents. We obtain an extension theorem for holomorphic jet sections of nef holomorphic vector bundle on compact Kähler manifolds. Using it we prove that Fano manifolds with strong Griffiths nef tange…

Projective manifolds with specific bundles are isomorphic to simpler spaces.

Fundamental groups of certain Kähler orbifolds have polynomial growth.

Paper proves structure of compact Kähler 3-folds with specific bundles.

Study Miyaoka-Yau inequality for certain projective manifolds.

Study the Albanese map for Kähler manifolds with nef anticanonical bundle.

In this paper, we study smooth complex projective varieties $X$ such that some exterior power $\bigwedge^r T_X$ of the tangent bundle is strictly nef. We prove that such varieties are rationally connected. We also classify the following two cases. If $T_X$ is strictly nef, then $X$ isomorphic to the projective space $\…

We classify compact Kähler manifolds with semi-positive holomorphic bisectional and big tangent bundles. We also classify compact complex surfaces with semi-positive tangent bundles and compact complex $3$-folds of the form $P(T^*X)$ whose tangent bundles are nef. Moreover, we show that if $X$ is a Fano manifold such t…

The paper establishes inequalities for Chern classes and numbers on polarized manifolds and nef vector bundles.

The paper studies fundamental groups of compact Kahler varieties with nef anti-canonical bundles.

Study compact Kähler manifolds with pseudo-effective tangent bundles.

The paper studies foliations on smooth projective varieties and their properties.

Study of tangent bundle positivity on complex projective varieties.

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

Study geodesics on a modified cotangent bundle over Kählerian manifolds.

Alternative proof of semipositivity and nefness for K-semistable log-Fano pairs.

Study on Kähler manifolds with non-positive mixed curvature and its implications.

In 1998, Gompf described a Stein domain structure on the disk cotangent bundle of any closed surface S, by a Legendrian handlebody diagram. We prove that Gompf's Stein domain is symplectomorphic to the disk cotangent bundle equipped with its canonical symplectic structure and the boundary of this domain is contactomorp…

Researchers prove existence of cscK metrics on smooth minimal models.

Two types of nonvanishing results are presented for compact Kähler varieties.

Study on Klein bottle's cotangent bundle using contact homology.

We obtain the natural diagonal almost product and locally product structures on the total space of the cotangent bundle of a Riemannian manifold. We find the Riemannian almost product (locally product) and the (almost) para-Hermitian cotangent bundles of natural diagonal lift type. We prove the characterization theorem…

Study on a weaker curvature condition for Kähler manifolds.

Researchers create a new metric on complex projective space bundles.

Study natural foliations in cotangent bundles of Cartan spaces.

Unique symplectic fillings of odd spheres' cotangent bundles proven.

We construct a Kaehler structure on the punctured cotangent bundle of the Cayley projective plane whose Kaehler form coincides with the natural symplectic form on the cotangent bundle and we show that the geodesic flow action is holomorphic and is expressed in a quite explicit form. We also give an embedding of the pun…

The study realizes symmetric spaces as cotangent bundles and finds nonnegative curvature examples.

Miyaoka-Yau inequality proven for smooth minimal models.

This article concerns cotangent-lifted Lie group actions; our goal is to find local and ``semi-global'' normal forms for these and associated structures. Our main result is a constructive cotangent bundle slice theorem that extends the Hamiltonian slice theorem of Marle, Guillemin and Sternberg. The result applies to a…

We describe a Lefschetz fibration of genus one on the disk cotangent bundle of any closed orientable surface S. As a corollary, we obtain an explicit genus one open book decomposition adapted to the canonical contact structure on the unit cotangent bundle of S.

Paper proves stability of flow in cotangent bundle for special Lagrangian submanifolds.

Introduce generalized Ueda obstruction classes for line bundles and apply them to non-semi-positivity.

Estimates Lelong numbers of Monge-Ampère products for Kähler manifolds.

Paper proves Hermitian-Yang-Mills metrics for stable Kähler bundles.

We construct some lift of an almost complex structure to the cotangent bundle, using a connection on the base manifold. This generalizes the complete lift defined by I.Sato and the horizontal lift introduced by K.Yano and S.Ishihara. We study some geometric properties of this lift and its compatibility with symplectic …

We describe an explicit open book decomposition adapted to the canonical contact structure on the unit cotangent bundle of a compact surface.

The paper classifies metrics on a Heisenberg group's cotangent bundle.