Related papers: Remarks on Seshadri constants

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 prove new results on single point Seshadri constants for ample line bundles on hyperelliptic surfaces. Given a hyperelliptic surface $X$ and an ample line bundle $L$ on $X$, we show that the least Seshadri constant $\varepsilon(L)$ of…

We prove two new results for Seshadri constants on surfaces of general type. Let $X$ be a surface of general type. In the first part, inspired by \cite{B-S}, we list the possible values for the multi-point Seshadri constant…

We give a bound for the multiple Seshadri constants on surfaces with Picard number 1. The result is a natural extension of the bound of A. Steffens for simple Seshadri constants. In particular, we prove that the Seshadri constant…

Let $X$ be a smooth projective surface with Picard number 1. Let $L$ be the ample generator of the N\'eron-Severi group of $X$. Given an integer $r\ge 2$, we prove lower bounds for the Seshadri constant of $L$ at $r$ general points in $X$.

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 study Seshadri constants of the canonical bundle on minimal surfaces of general type. First, we prove that if the Seshadri constant $\eps(K_X,x)$ is between 0 and 1, then it is of the form $(m-1)/m$ for some integer $m\ge 2$. Secondly,…

Let $X$ be a complex nonsingular projective surface and let $L$ be an ample line bundle on $X$. We study multi-point Seshadri constants of $L$ at singular points of certain arrangements of curves on $X$. We pose some questions about such…

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…

Let $X$ be a projective surface and let $L$ be an ample line bundle on $X$. The global Seshadri constant $\varepsilon(L)$ of $L$ is defined as the infimum of Seshadri constants $\varepsilon(L,x)$ as $x\in X$ varies. It is an interesting…

We compute Seshadri constants $\eps(X):= \eps(\O_X(1))$ on $K3$ surfaces $X$ of degrees 6 and 8. Moreover, more generally, we prove that if $X$ is any embedded $K3$ surface of degree $2r-2 \geq 8$ in $\PP^r$ not containing lines, then $1 <…

Let $X_r$ denote the blow-up of the hyperelliptic surface $X$ at $r$ very general points. In this paper, we first provide a criterion for the ampleness of a line bundle on $X_r$ and compare it with an existing result. We then study the…

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…

Let $X$ be a smooth variety and let $L$ be an ample line bundle on $X$. If $\pi^{alg}_{1}(X)$ is large, we show that the Seshadri constant $\epsilon(p^{*}L)$ can be made arbitrarily large by passing to a finite \'etale cover…

Consider a polarized abelian variety $(A,L)$ over the field of complex numbers. Following Demailly, one can associate to $(A,L)$ a real number $\epsilon(A,L)$, its {\em Seshadri constant}, which in effect measures how much of the positivity…

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…

The aim of this note is to study local and global Seshadri constants for a family of smooth surfaces with prescribed polarization. We shall first observe that given $\alpha$ being smaller than the square root of the degree of polarization,…

For a positive integer $n$, let $X_n \to X_{n-1} \to \ldots \to X_2 \to X_1 \to X_0$ be a Bott tower of height $n$, and let $L$ be a nef line bundle on $X_n$. We compute Seshadri constants $\varepsilon(X_n,L,x)$ of $L$ at any point $x \in…

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 $L$ be a nef line bundle on a smooth complex projective variety $X$ of dimension $n$. Demailly has introduced a very interesting invariant --- the Seshadri constant $\epsilon(L,x)$ --- which in effect measures how positive $L$ is…