Related papers: Seshadri constants on abelian surfaces

Seshadri constants on abelian surfaces are fully understood in the case of Picard number one. Little is known so far for simple abelian surfaces of higher Picard number. In this paper we investigate principally polarized abelian surfaces…

The purpose of this paper is to study Seshadri constants on the self-product $E\times E$ of an elliptic curve $E$. We provide explicit formulas for computing the Seshadri constants of all ample line bundles on the surfaces considered. As an…

Given an etale quotient q:X->Y of smooth projective varieties we relate the simple Seshadri constant of a line bundle M on Y with the multiple Seshadri constant of q*M in the points of the fiber. We apply this method to compute the Seshadri…

We prove that the Seshadri constant of a polarized abelian variety is equal to the Seshadri constant of its abelian subvariety if the Seshadri constant is relatively small with respect to its degree, or it contains an abelian divisor which…

Seshadri constants are local invariants, introduced by Demailly, which measure the local positivity of ample line bundles. Recent interest in Seshadri constants stems on the one hand from the fact that bounds on Seshadri constants yield,…

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…

In this paper we consider the question of when Seshadri constants on abelian surfaces are integers. Our first result concerns self-products $E\times E$ of elliptic curves: If $E$ has complex multiplication in $\Z[i]$ or in…

Let $X$ be a smooth complex projective curve and let $E$ be a vector bundle on $X$ which is not semistable. We consider a flag bundle $\pi: \text{Fl}(E) \to X$ parametrizing certain flags of fibers of $E$. The dimensions of the successive…

Let $X = \mathbb{P}(E_1) \times_C \mathbb{P}(E_2)$ where $C$ is a smooth curve and let $E_1$, $E_2$ be vector bundles over $C$. In this paper, we extend the results in \cite{K-M-R} by computing the nef cone of $X$ without restriction on the…

We compute Seshadri constants of a torus equivariant nef vector bundle on a projective space satisfying certain conditions. As an application, we compute Seshadri constants of tangent bundles on projective spaces. We also consider…

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…

We study Seshadri constants of ample line bundles on hyperelliptic surfaces. We obtain new lower bounds and compute the exact values of Seshadri constants in some cases. Our approach uses results of F. Serrano (1990), B. Harboune and J. Roe…

In this note we improve a result of Steffens on the lower bound for Seshadri constants in very general points of a surface with one-dimensional N\'eron-Severi space. We also show a multi-point counterpart of such a lower bound.

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…

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 study lower bounds on Seshadri constants at arbitrary points on surfaces with Picard number 1.

In this article, we give a description of the closed cone of curves of the projective bundle $\mathbb{P}(E)$ over a smooth projective variety $X$. Using duality, we then calculate the nef cone of divisors in $\mathbb{P}(E)$ over some…

We examine how the Seshadri constant of an ample line bundle at a very general point of an algebraic surface can carry important global geometric information about the surface. In particular, we obtain a numerical criterion for when a…

Starting with the pioneering work of Ein and Lazarsfeld restrictions on values of Seshadri constants on algebraic surfaces have been studied by many authors. In the present note we show how approximation involving continued fractions…

We study a Seshadri constant at a general point on a rational surface whose anticanonical linear system contains a pencil. First, we describe a Seshadri constant of an ample line bundle on such a rational surface explicitly by the numerical…