Related papers: On the valuative Nagata conjecture

We provide a lower bound on the degree of curves of the projective plane $\mathbb{P}^2$ passing through the centers of a divisorial valuation $\nu$ of $\mathbb{P}^2$ with prescribed multiplicities, and an upper bound for the Seshadri-type…

It is well known that multi-point Seshadri constants for a small number $s$ of points in the projective plane are submaximal. It is predicted by the Nagata conjecture that their values are maximal for $s\geq 9$ points. Tackling the problem…

We study the Seshadri constants of cyclic coverings of smooth surfaces. The existence of an automorphism on these surfaces can be used to produce Seshadri exceptional curves. We give a bound for multiple Seshadri constants on cyclic…

T. Szemberg proposed in 2001 a generalization to arbitrary varieties of M. Nagata's 1959 open conjecture, which claims that the Seshadri constant of r>9 very general points of the projective plane is maximal. Here we prove that Nagata's…

We develop a new approach towards obtaining lower bounds of the Seshadri constants of ample adjoint divisors on smooth projective varieties $X$ in arbitrary characteristic. Let $x\in X$ be a closed point and $A$ an ample divisor on $X$. If…

We consider the last value $\hat{\mu} (\nu)$ of the vanishing sequence of $H^0(L)$ along a divisorial or irrational valuation $\nu$ centered at $\mathcal{O}_{\mathbb{P}^2,p}$, where $L$ resp. $p$ is a line resp. a point of the projective…

In "Seshadri fibrations of algebraic surfaces" [arXiv:0709.2592v1] we showed that if the multiple point Seshadri constants of an ample line bundle on a smooth projective surface in very general points satisfy certain inequality then the…

Fujita's conjecture is known to be false in positive characteristic. We conjecture and give an approach to a new variant of Fujita's conjecture for the basepoint-freeness, very ampleness, and jet ampleness of linear systems of the form…

Working over C, we show that, apart possibly from a unique limit point, the possible values of multi-point Seshadri constant for general points on smooth projective surfaces form a discrete set. In addition to its theoretical interest, this…

In this paper we present a way of computing the degree of the secant (resp., tangent) variety of a smooth projective surface, under the assumption that the divisor giving the embedding in the projective space is $3$-very ample. This method…

We study Seshadri constants of certain ample vector bundles on projective varieties. Our main motivation is the following question: Under what conditions are the Seshadri constants of ample vector bundles at least 1 at all points of the…

We formulate Vojta's conjecture for smooth weighted projective varieties, weighted multiplier ideal sheaves, and weighted log pairs and prove that all three versions of the conjecture are equivalent. In the process, we introduce generalized…

Motivated by a similar result of Dumnicki, K\"uronya, Maclean and Szemberg under a slightly stronger hypothesis, we exhibit irrational single-point Seshadri constants on a rational surface $X$ obtained by blowing up very general points of…

A broadly applicable geometric approach for constructing nef divisors on blow ups of algebraic surfaces at n general points is given; it works for all surfaces in all characteristics for any n. This construction is used to obtain…

We prove that an $n$-dimensional complex projective variety is isomorphic to $\mathbb{P}^n$ if the Seshadri constant of the anti-canonical divisor at some smooth point is greater than $n$. We also classify complex projective varieties with…

We introduce Seshadri constants for line bundles in a relative setting. They generalize the classical Seshadri constants of line bundles on projective varieties and their extension to vector bundles studied by Beltrametti-Schneider-Sommese…

Let $X$ be a surface and let $L$ be an ample line bundle on $X$. We first obtain a lower bound for the Seshadri constant $\varepsilon(X,L,r)$, when $r \ge 3$. We then assume that $X$ is a ruled surface and study Seshadri constants on $X$ in…

We develop a local positivity theory for movable curves on projective varieties similar to the classical Seshadri constants of nef divisors. We give analogues of the Seshadri ampleness criterion, of a characterization of the augmented base…

In this note we contribute to the study of Seshadri constants on abelian and bielliptic surfaces. We specifically focus on bounds that hold on all such surfaces, depending only on the self-intersection of the ample line bundle under…

We prove that projectivity is an open condition for deformations of algebraic spaces with rational singularities. V.2: references updated and corrected.