Related papers: Manifolds with nef cotangent bundle

Let $X$ be a projective Fano manifold of Picard number one, different from the projective space. There is a folklore conjecture that any non-constant endomorphism of $X$ is an isomorphism. In the first half of this article, we will prove…

We investigate the universal cover of projective threefolds whose tangent bundle is a direct sum of subbundles in case the Kodaira dimension is not 1 and 2. We also prove results on Fano manifolds with splitting tangent bundles in any…

We present a smooth, complete toric threefold with no nontrivial nef line bundles. This is a counterexample to a recent conjecture of Fujino.

In the first part of this note, we discuss the compact K\"ahler manifold with a strongly pseudo-effective tangent bundle. In the second part, we give new proof of the fact that the only projective manifolds with the big tangent bundle are…

On a projective surface it is well-known that the set of curves orthogonal to a nef line bundle is either finite or uncountable. We show that this dichotomy fails in higher dimension by constructing a nef line bundle on a threefold which is…

The present paper concerns the invariants of generically nef vector bundles on ruled surfaces. By Mehta - Ramanathan Restriction Theorem and by Miyaoka characterization of semistable vector bundles on a curve, the generic nefness can be…

As a natural extension of the theory of uniform vector bundles on Fano manifolds, we consider uniform principal bundles, and study them by means of the associated flag bundles, as their natural projective geometric realizations. In this…

We show that a compact Kahler manifold with nonpositive holomorphic sectional curvature has nef canonical bundle. If the holomorphic sectional curvature is negative then it follows that the canonical bundle is ample, confirming a conjecture…

In this paper we study the positivity of the cotangent bundle of projective manifolds. We conjecture that the cotangent bundle is pseudoeffective if and only the manifold has non-zero symmetric differentials. We confirm this conjecture for…

Let $X$ be a complex smooth projective variety such that the exterior power of the tangent bundle $\bigwedge^{r} T_X$ is nef for some $1\leq r<\dim X$. We prove that, up to an \'etale cover, $X$ is a Fano fiber space over an Abelian…

In this paper, we prove the Bogomolov-Gieseker type inequality conjecture for threefolds with nef tangent bundles. As a corollary, there exist Bridgeland stability conditions on these threefolds.

Given an almost complex structure on a subbundle of the cotangent bundle, we prove a Castelnuovo--de Franchis type theorem for it.

We prove that the Albanese map of a smooth projective threefold, whose anticanonical bundle is nef, is a surjective submersion. We also investigate morphisms of threefolds to curves and surfaces whose relative anticanonical bundle are nef.

In this paper we prove the following abundance-type result: for any smooth Fano variety $X$, the tangent bundle $T_X$ is nef if and only if it is big and semiample in the sense that the tautological line bundle…

Suppose that $X$ is a projective manifold whose tangent bundle $T_X$ contains a locally free strictly nef subsheaf. We prove that $X$ is isomorphic to a projective bundle over a hyperbolic manifold. Moreover, if the fundamental group…

In this paper we classify rank two Fano bundles $\cE$ on Fano manifolds satisfying $H^2(X,\Z)\cong H^4(X,\Z)\cong\Z$. The classification is obtained via the computation of the nef and pseudoeffective cones of the projectivization…

Much inspired by J. A. Wi\'sniewski's nef-value function method, we prove that in a smooth projective family over the unit disk, if the adjoint bundle of the canonical line bundle with a relatively semiample line bundle is nef on one fiber,…

In this article, we investigate Serrano's conjecture for strictly nef divisors on projective bundles over higher dimensional smooth projective varieties.

We define a subcategory of the category of diffeological spaces, which contains smooth manifolds, the diffeomorphism subgroups and its coadjoint orbits. In these spaces we construct a tangent bundle, vector fields and a de Rham cohomology.

We obtain a sufficient condition for a Fano threefold with terminal singularities to have a conic bundle structure.