Related papers: Numerical characterization of nef arithmetic divis…

The volume of a Cartier divisor on a projective variety is a nonnegative real number that measures the asymptotic growth of sections of multiples of the divisor. It is known that the set of these numbers is countable and has the structure…

Let $X'$ be a complex projective manifold, $\dim X'>1$, $Z$ a connected analytic subset of codimension one which is the support of a nef effective Cartier divisor $D$ on $X'$, $X:=X'\setminus Z$. Let $\kappa(D)$ be the Iitaka dimension of…

Let $C$ be a smooth projective curve over $\mathbb C$. Let $n,d\geq 1$. Let $\mathcal Q$ be the Quot scheme parameterizing torsion quotients of the vector bundle $\mathcal O^n_C$ of degree $d$. In this article we study the nef cone of…

We study effective divisors $D$ on surfaces with $H^0(\mathcal O_D)=k$ and $H^1(\mathcal O_D)=H^0(\mathcal O_D(D))=0$. We give a numerical criterion for such divisors, following a general investigation of negativity, rigidity and…

The purpose of this paper is to modify the notion of the Nevanlinna constant $\operatorname{Nev}(D)$, recently introduced by the first author, for an effective Cartier divisor on a projective variety $X$. The modified notion is called the…

In these notes we investigate the cone of nef curves of projective varieties, which is the dual cone to the cone of pseudo-effective divisors. We prove a structure theorem for the cone of nef curves of projective $\mathbb Q$-factorial klt…

We prove that a regular projective surface $S$ over a field $k$ of characteristic $p \ge 7$, with $H^0(S,\mathcal{O}_S) = k$ and $-K_S$ being nef, is geometrically integral over $k$.

Let k be an algebraically closed field complete with respect to a non-Archimedean absolute value of arbitrary characteristic. Let D_1,...,D_n be effective nef divisors intersecting transversally in an n-dimensional nonsingular projective…

Let $L$ be a line bundle on a scheme $X$, proper over a field. The property of $L$ being nef can sometimes be "thickened", allowing reductions to positive characteristic. We call such line bundles arithmetically nef. It is known that a line…

Using currents with minimal singularities, we construct pointwise minimal multiplicities for a real pseudo-effective $(1,1)$-class $\alpha$ on a compact complex $n$-fold $X$, which are the local obstructions to the numerical effectivity of…

Let M_g be the moduli space of smooth curves of genus g >= 3, and \bar{M}_g the Deligne-Mumford compactification in terms of stable curves. Let \bar{M}_g^{[1]} be an open set of \bar{M}_g consisting of stable curves of genus g with one node…

A result of Belyi can be stated as follows. Every curve defined over a number field can be expressed as a cover of the projective line with branch locus contained in a rigid divisor. We define the notion of geometrically rigid divisors in…

We give a direct proof, valid in arbitrary characteristic, of nefness for two families of F-nef divisors on $\bar{M}_{0,n}$. The divisors we consider include all type A level one conformal block divisors as well as divisors previously not…

Let $X$ be a smooth projective variety with a nef anticanonical divisor over an algebraically closed field of characteristic $p>0$. In this paper, we establish a precise structure of $X$ under the condition that $a_X: X \to {\rm Alb}(X)$ is…

We prove lower bounds for the minimum distance of algebraic geometry codes over surfaces whose canonical divisor is either nef or anti-strictly nef and over surfaces without irreducible curves of small genus. We sharpen these lower bounds…

An integer $n$ is said to be \textit{arithmetic} if the arithmetic mean of its divisors is an integer. In this paper, using properties of the factorization of values of cyclotomic polynomials, we characterize arithmetic numbers. As an…

In this paper, we study effective, nef and semiample cones of surfaces isogenous to a product of mixed type with $p_g=0$. In particular, we prove that all reducible fake quadrics are Mori dream surfaces.

We carry out a detailed intersection theoretic analysis of the Deligne-Mumford compactification of the divisor on M_{10} consisting of curves sitting on K3 surfaces. This divisor is not of classical Brill-Noether type, and is known to give…

We compute divisors class groups of singular surfaces. Most notably we produce an exact sequence that relates the Cartier divisors and almost Cartier divisors of a surface to the those of its normalization. This generalizes Hartshorne's…

We prove that any nef b-divisor class on a projective variety defined over an algebraically closed field of characteristic 0 is a decreasing limit of nef Cartier classes. Building on this technical result, we construct an intersection…