相关论文: Fujita's conjecture for quasi-elliptic surfaces

For $\theta$ a non-algebraic point on a quasi projective variety over a number field, I prove that $\theta$ has an approximation by a series of algebraic points of bounded height and degree which is essentially best possible. Applications…

We prove Iitaka's $C_{n,m}$ conjecture for $3$-folds over the algebraic closure of finite fields. Along the way we prove some results on the birational geometry of log surfaces over nonclosed fields and apply these to existence of relative…

The result on 3-fold is now optimal by the result of Ein-Lazarsfeld and Helmke.

We prove, with no claim to originality, a relative version of the Fujita-Zariski theorem. When the base is a field, this result is due to Fujita (1983) and states that if an invertible sheaf on a proper variety is ample on its base locus,…

We prove the filling area conjecture in the hyperelliptic case. In particular, we establish the conjecture for all genus 1 fillings of the circle, extending P. Pu's result in genus 0. We translate the problem into a question about closed…

We establish the following uniformization result for metric spaces $X$ of finite Hausdorff 2-measure. If $X$ is homeomorphic to a smooth 2-manifold $M$ with non-empty boundary, then we show that $X$ admits a quasiconformal almost…

We give a proof of the Morrison-Kawamata cone conjecture for Enriques surfaces independent of their characteristic. It is based on the analysis of certain generically finite morphisms of degree two.

An asymptotic formula is established for the number of rational points of bounded height on a non-singular quartic del Pezzo surface with a conic bundle structure.

We give a proof the monodromy conjecture relating the poles of motivic zeta functions with roots of b-functions for isolated quasihomogeneous hypersurfaces, and more generally for semi-quasihomogeneous hypersurfaces. We also give a strange…

Let X be a smooth quartic surface not containing lines, defined over a number field K. We prove that there are only finitely many bitangents to X which are defined over K. This result can be interpreted as saying that a certain surface,…

We give the new effective criterion for the global generation of the adjoint bundle on normal surfaces with a boundary. We could make the invariant \delta small a bit more on log-terminal singular point, and then we could prove the theorem…

In this work we prove on a given smooth toric threefold all but finitely many ample line bundles are projectively normal.

We prove that if a complete Riemannian surface $(\Sigma,d_\Sigma)$ is quasi-isometric to some bounded degree graph $G$, then $\Sigma$ admits a triangulation whose 1-skeleton is quasi-isometric to it when equipped with the simplicial metric.…

We prove that the transcendental motive of any quasi elliptic surface is trivial. To prove this, we focus on the uniruledness of quasi elliptic surfaces.

It is shown that the weak multidimensional Suita conjecture fails for any bounded non-pseudoconvex domain with $C^{1+\varepsilon_-}$-smooth boundary. On the other hand, it is proved that the weak converse to the Suita conjecture holds for…

We show that if the Atiyah Jones conjecture holds for a surface $X,$ then it also holds for the blow-up of $X$ at a point. Since the conjecture is known to hold for ${\mathbb P}^2$ and for ruled surfaces, it follows that the conjecture is…

Solving a long-standing open question in convex geometry, we will show that typical convex surfaces contain points of infinite curvature in all tangent directions. To prove this, we use an easy curvature definition imitating the idea of…

Let X be a smooth projective surface over C and let L be an ample line bundle on X. In this note, we show that, for all sufficiently large d, any number of general double points on X imposes the expected number of conditions on the linear…

Fujita's second theorem for K\"ahler fibre spaces over a curve asserts that the direct image $V$ of the relative dualizing sheaf splits as the direct sum $ V = A \oplus Q$, where $A$ is ample and $Q$ is unitary flat. We focus on our…

We establish a criterion that ensures a bounded almost complex curve in a bounded almost complex 4-manifold minimizes genus amongst all smooth surfaces that share its homology class and the transverse link on its boundary. An immediate…