Related papers: Numerical trivial fibrations

We discuss the flatness property of some fiber type contractions of complex smooth projective varieties of arbitrary dimensions. We relate the flatness of some morphisms having one-dimensional fibers with their conic bundles structures,…

Let G/Q be an homogeneous variety embedded in a projective space P thanks to an ample line bundle L. Take a projective space containing P and form the cone X over G/Q, we call this a cone over an homogeneous variety. Let $\alpha$ a class of…

This paper investigates the projectivization of real vector bundles over small covers. We first give a necessary and sufficient condition for such a projectivization to be a small cover. Then associated with moment-angle manifolds, we…

After recalling the definition and basic properties of Ulrich bundles, we focus on the existence problem: does any smooth projective variety carry a Ulrich bundle? We show that the Serre construction provides a positive answer on certain…

We investigate the properties of a specific quotient space construction, the "warped projection'" $\pi: W_\alpha \to D_\alpha$, over a smoothly contractible base. In a previous version of this work, it was claimed that this structure…

In this paper, we prove that a compact K\"ahler manifold $X$ with pseudo-effective (resp. singular positively curved) tangent bundle admits a smooth (resp. locally constant) rationally connected fibration $\phi \colon X \to Y$ onto a finite…

Let $\pi\,:\, X \,\longrightarrow\, Y$ be a finite morphism of smooth projective varieties defined over an algebraically closed field of characteristic zero. We study the necessary and sufficient criteria for $\pi$ such that there exists a…

We study effective global generation properties of projectivizations of curve semistable vector bundles over curves and abelian varieties.

Lasell and Ramachandran show that the existence of rational curves of positive self-intersection on a smooth projective surface $X$ implies that all the finite dimensional linear representations of the fundamental group $\pi_1(X)$ are…

We describe the structure of regular codimension $1$ foliations with numerically projectively flat tangent bundle on complex projective manifolds of dimension at least $4$. Along the way, we prove that either the normal bundle of a regular…

The aim of this paper is twofold. First we prove a theorem of extension of sections of a coherent subquotient of a hermitian vector bundle on a complex analytic space with control of the norms, without any of the smoothness assumptions that…

We prove an effective upper bound on the number of effective sections of a hermitian line bundle over an arithmetic surface. It is an effective version of the arithmetic Hilbert--Samuel formula in the nef case. As a consequence, we obtain…

In the present article we work out a relative setup of generic structures on surface singularities. We fix an analytic type on a subgraph of a rational homology sphere resolution graph $\mathcal{T}$ and we choose a relatively generic normal…

In an earlier paper we conjectured a relation between the quantum $\mathcal D$-modules of a smooth variety $X$ and the projectivisation of a direct sum of line bundles over it. In this paper we prove the conjecture when $X$ is a complete…

We give several structure theorems for certain surjective endomorphisms on Mori fibre spaces, based on the dynamical Iitaka fibration of the ramification divisor. As an application, we prove the Kawaguchi-Silverman conjecture for projective…

We classify smooth complex projective varieties $X \subset \proj^N$ of dimension $2s+1$ containing a linear subspace $\Lambda$ of dimension $s$ whose normal bundle $N_{\Lambda/X}$ is numerically effective.

In this paper, we study almost nef regular foliations. We give a structure theorem of a smooth projective variety $X$ with an almost nef regular foliation $\mathcal{F}$: $X$ admits a smooth morphism $f: X \rightarrow Y$ with rationally…

Any smooth projective variety contains many complete intersection subvarieties with ample cotangent bundles, of each dimension up to half its own dimension.

We use sets of trivial line bundles for the realization of gerbes. For 1-gerbes the structure arises naturally for the Weyl fermion vacuum bundle at a fixed time. The Schwinger term is an obstruction in the triviality of a 1-gerbe.

Consider the scheme parametrizing non-constant morphisms from a fixed projective curve to a projective surface. There is a rational map between this scheme and the Chow variety of $1$-cycles on the surface. We prove that, if the curve is…