Related papers: A numerical ampleness criterion via Gale duality

In this paper, we prove the ampleness conjecture and Serrano's conjecture for strictly nef divisors on K-trivial fourfolds. Specifically, we show that any strictly nef divisors on projective fourfolds with trivial canonical bundle and…

In their work, Serre and Swinnerton-Dyer study the congruence properties of the Fourier coefficients of modular forms. We examine similar congruence properties, but for the coefficients of a modified Taylor expansion about a CM point…

For a fixed positive integer d, we show the existence of the limiting gap distribution measure for the sets of Farey fractions a/q of order Q with a not divisible by d, and respectively with q relatively prime with d, as Q tends to…

Using Weil descent, we give bounds for the number of rational points on two families of curves over finite fields with a large abelian group of automorphisms: Artin-Schreier curves of the form $y^q-y=f(x)$ with $f\in\Fqr[x]$, on which the…

We give a characterization of Gorenstein toric Fano varieties of dimension $n$ with index $n$ among toric varieties. As an application, we give a strong version of Fujita's freeness conjecture and also give a simple proof of Fujita's very…

We consider the problem of counting the number of varieties in a family over a number field which contain a rational point. In particular, for products of Brauer-Severi varieties and closely related counting functions associated to Brauer…

We revisit results of Fujino--Sato on complete non-projective $\mathbb Q$-factorial toric varieties and their conjectural factorization by flips. We show that their main results admit short conceptual proofs, avoiding any restriction on the…

We establish a criterion for a complex number to be algebraic over Q of degree at most two. It requires that, for any sufficiently large real number X, there exists a non-zero polynomial with integral coefficients, of degree at most two and…

We describe a class of toric varieties in the $N$-dimensional affine space which are minimally defined by no less than $N-2$ binomial equations.

This paper studies the structure of the Mordell--Weil groups of semiabelian varieties over algebraic extensions of number fields whose absolute Galois group is finitely generated, with particular emphasis on that generated by a single…

This is an addendum to our earlier paper on the defect of an ample divisor of an abelian variety. It modifies an argument of the original paper to handle one difficulty there. At the same time the modification improves the result in the…

In this note we improve the theorem on Galois rational covers $X\dashrightarrow V$ for primitive Fano varieties $V$, recently proven by the author, in the two directions: we extend to the maximum the class of Galois groups $G$, for which…

We address the question of effectivity for calculation of local Weil functions from the viewpoint of presentations of Cartier divisors. This builds on the approach of Bombieri and Gubler as well as the perspective of our earlier works.…

An extension to higher dimensions of the Bel-Debever characterization of the Weyl tensor is considered. This provides algebraic conditions that uniquely determine the multiplicity of a Weyl aligned null direction (WAND), and thus the…

In this article we prove a finiteness result on the number of log minimal models for $3$-folds in char $p>5$. We then use this result to prove a version of Batyrev's conjecture on the structure of nef cone of curves on $3$-folds in…

We show NP-completeness for several planar variants of the monotone satisfiability problem with bounded variable appearances. With one exception the presented variants have an associated bipartite graph where the vertex degree is bounded by…

For a normal projective variety $X$, the $\bf Q$-factoriality defect $\sigma(X)$ is defined to be the rank of the quotient of the group of Weil divisors by the subgroup of Cartier ones. We prove a slight improvement of a topological formula…

We prove the (equivariant) noetherian property for a wide class of varieties generalizing the class of Plucker varieties (Theorem 1). It improves previous results of Draisma-Eggermont who treated the case of bounded Plucker varieties. Key…

This paper treats the problem of determining conditions for the Fourier coefficients of a Maass-Hecke newform at cusps other than infinity to be multiplicative. To be precise, the Fourier coefficients are defined using a choice of matrix in…

We study issues related to F-theory on Calabi-Yau fourfolds and its duality to heterotic theory for Calabi-Yau threefolds. We discuss principally fourfolds that are described by reflexive polyhedra and show how to read off some of the data…