Related papers: Abundance theorem for surfaces over imperfect fiel…

In this paper we prove a desingularization theorem for Legendrian surfaces that are the conormal of a quasi-ordinary hypersurface.

The ruled residue theorem characterises residue field extensions for valuations on a rational function field. Under the assumption that the characteristic of the residue field is different from $2$ this theorem is extended here to function…

Given a covering of the projective line with ramifications defined over a number field, we define a plain model of the algebraic curve realizing the Riemann existence theorem for this covering, and bound explicitly the defining equation of…

On a smooth asymptotically flat Riemannian manifold with non-compact boundary, we prove a positive mass theorem for metrics which are only continuous across a compact hypersurface. As an application, we obtain a positive mass theorem on…

Given a graded sequence of ideals (a_m) on a smooth variety $X$ having finite log canonical threshold, suppose that for every m we have a divisor E_m over X that computes the log canonical threshold of a_m, and such that the log…

Let $\mathcal C\subset(0,1]$ be a set satisfying the descending chain condition. We show that any accumulation point of volumes of log canonical surfaces $(X, B)$ with coefficients in $\mathcal C$ can be realized as the volume of a log…

In this note, we construct three new infinite families of surfaces of general type with canonical map of degree 2 onto a surface of general type. For one of these families the canonical system has base points.

We study the existence problem and the enumeration problem for sections of Serre fibrations over compact orientable surfaces. When the fundamental group of the fiber is finite, a complete solution is given in terms of 2-dimensional…

We present a new topological proof of the infinitude of prime numbers with a new topology. Furthermore, in this topology, we characterize the infinitude of any non-empty subset of prime numbers.

Building on results of Koll\'ar, we prove Shokurov's ACC Conjecture for log canonical thresholds on smooth varieties, and more generally, on varieties with quotient singularities.

We determine the minimal possible volume of a projective log canonical surface of general type with prescribed positive geometric genus. As applications, we provide effecitive Noether type inequalities for log canonical threefolds and…

We construct a normal projective $\mathbb{Q}$-Gorenstein surface over an algebraically closed field whose canonical ring is not finitely generated. Moreover, we provide a counterexample to the minimal model program for…

We study the question of finding smooth hyperplane sections to a pencil of hypersurfaces over finite fields.

We show that the Sarkisov program holds for $\mathbb{Q}$-factorial log surfaces and log canonical surfaces over any algebraically closed field.

We show a Lefschetz theorem for irreducible overconvergent $F$-isocrystals on smooth varieties defined over a finite field. We derive several consequences from it.

The set of volumes of stable surfaces does have accumulation points. In this paper, we study this phenomenon for surfaces with one cyclic quotient singularity, towards answering the question under which conditions we can still have…

In this note, we find a new way to prove several properties of 2-alternating capacities.

We present an adequacy theorem for a concurrent extension of probabilistic GCL. The underlying denotational semantics is based on the so-called mixed powerdomains, which combine non-determinism with probabilistic behaviour. The theorem…

In this paper, we construct counterexamples to the boundedness of generalised log canonical models of surfaces with fixed appropriate invariants, where the underlying varieties can have arbitrary Kodaira dimension. This answers a question…

In this paper, we study residues of differential 2-forms on a smooth algebraic surface over an arbitrary field and give several statements about sums of residues. Afterwards, using these results we construct algebraic-geometric codes which…