Related papers: Varieties with generically nef tangent bundles

In this paper we derive a list of all the possible indecomposable normalized rank--two vector bundles without intermediate cohomology on the prime Fano threefolds and on the complete intersection Calabi Yau threefolds, say $V$, of Picard…

We give the first examples of flat fiber type contractions of Fano manifolds onto varieties that are not weak Fano, and we prove that these morphisms are Fano conic bundles. We also review some known results about the interaction between…

We compare the behaviour of entire curves and integral sets, in particular in relation to locally trivial fiber bundles, algebraic groups and finite ramified covers over semi-abelian varieties.

In this paper, we prove that for any weak Del Pezzo surface $S$ of degree at least $4$, the tangent bundle $T_S$ is almost nef. For the proof, we use total dual VMRTs induced by conic bundle structures.

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

We study the cones of q-ample divisors on smooth complex varieties. In favourable cases, we identify a part where the closure of this cone and the nef cone have the same boundary. This is especially interesting for Fano (or almost Fano)…

A linear F-manifold is an F-manifold (E, \circ , e) defined on the total space of a vector bundle \pi : E \rightarrow M for which the multiplication and unit field are linear tensor fields. We develop a systematic treatment of linear…

Let X be a Fano manifold with Picard number one such that the tangent bundle T_X is big. If X admits a rational curve with trivial normal bundle, we show that X is isomorphic to the del Pezzo threefold of degree five.

On a compact K\"ahler manifold, we introduce a notion of almost nonpositivity for the holomorphic sectional curvature, which by definition is weaker than the existence of a K\"ahler metric with semi-negative holomorphic sectional curvature.…

Logarithmic and $b$-tangent bundles provide a versatile framework for addressing singularities in geometry. Introduced by Deligne and Melrose, these modified bundles resolve singularities by reframing singular vector fields as well-behaved…

We consider slope stability of the canonical extension of the tangent bundle by the trivial line bundle and with the extension class c_1(T_X) on Picard-rank-1 Fano varieties. In cases where the index divides the dimension or the dimension…

We show that the category of affine bundles over a smooth manifold M is equivalent to the category of affine spaces modelled on projective finitely generated C^\infty(M)-modules. Using this equivalence of categories, we are able to give an…

We discuss the local freeness and the numerical semipositivity of direct images of relative pluricanonical bundles for surjective morphisms between smooth projective varieties with connected fibers. We give a desirable semipositivity…

Let $X$ be a smooth complex projective variety with nef $\bigwedge^2 T_X$ and $\dim X \geq 3$. We prove that, up to a finite \'etale cover $\tilde{X} \to X$, the Albanese map $\tilde{X} \to {\rm Alb}(\tilde{X})$ is a locally trivial…

S. Kov\'acs proposed a conjecture on rigidity results induced by ample subsheaves of some exterior power of tangent bundles for projective manifolds. We verify the conjecture in the case of second exterior products under a rank condition.…

We show that a nef and big line bundle whose adjoint bundle has non-zero global sections on a nonsingular toric weak Fano 3-fold is normally generated. As a consequence, we see that all ample line bundles on a nonsingular toric weak Fano…

Geodesically complete affine manifolds are quotients of the Euclidean space through a properly discontinuous action of a subgroup of affine Euclidean transformations. An equivalent definition is that the tangent bundle of such a manifold…

Let $X$ be a smooth projective curve defined over an algebraically closed field $k$, and let $E$ be a vector bundle on $X$. We compute the nef cone of any flag bundle associated to $E$.

We use Totaro's examples of non-semiample nef line bundles on smooth projective surfaces over finite fields to construct nef line bundles for which the first cohomology group cannot be killed by any generically finite covers. This is used…

We prove that under a finite surjective map of irreducible smooth complex projective curves, the pullback and direct image of a parabolic ample (respectively, parabolic nef) vector bundle is again parabolic ample (respectively, parabolic…