Related papers: Seshadri constants on Bott towers

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…

Let $X$ be a smooth projective variety defined over a field $k$ of characteristic $0$ and let $\mathcal{L}$ be a nef line bundle defined over $k$. We prove that if $x\in X$ is a $k$-rational point then the Seshadri constant $\epsilon(X,…

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…

Let $X$ be a complex projective variety, and let $E_{\ast}$ be a parabolic vector bundle on $X$. We introduce the notion of \textit{parabolic Seshadri constants} of $E_{\ast}$. It is shown that these constants are analogous to the classical…

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 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…

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…

Suppose D is an effective divisor on a smooth projective algebraic variety X. For each point x of X we associate a numberical invariant called the moving Seshadri constant of D at x which is a numerical measure of positivity of the divisor…

In the present paper we are concerned with the possible values of Seshadri constants. While in general every positive rational number appears as the local Seshadri constant of some ample line bundle, we point out that for adjoint line…

Given a nef and big line bundle $L$ on a projective variety $X$ of dimension $d \geq 2$, we prove that the Seshadri constant of $L$ at a very general point is larger than $(d+1)^{\frac{1}{d}-1}$. This slightly improves the lower bound $1/d$…

Let $e,r \ge 0$ be integers and let $\mathbb{F}_e : = \mathbb{P}(\mathcal{O}_{\mathbb{P}^1} \oplus \mathcal{O}_{\mathbb{P}^1}(-e))$ denote the Hirzebruch surface with invariant $e$. We compute the Seshadri constants of an ample line bundle…

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…

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…

In this article we compute Seshadri constants of ample line bundles on the blowup of Hirzebruch surface $\mathbb{F}_e$ at $r\leqslant e+3$ very general points. Similarly, we compute Seshadri constants on the blowups of certain decomposable…

We give the lower bound on Seshadri constants for the case of very ample line bundles on threefolds. We consider the situation when the Seshadri constant is strictly less than 2 and give a version of Bauer's theorem \cite[Theorem 2.1]{B1}…

We study torus-equivariant vector bundles $E$ on a complex projective variety $X$ which is either a Bott-Samelson-Demazure-Hansen variety or a wonderful compactification of a complex symmetric variety of minimal rank. We show that $E$ is…

So far, Seshadri constants on abelian surfaces are completely understood only in the cases of Picard number one and on principally polarized abelian surfaces with real multiplication. Beyond that, there are partial results for products 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…

Seshadri constants, introduced by Demailly, measure the local positivity of a nef divisor at a point. In this paper, we compute the Seshadri constants of the anticanonical divisors of Fano manifolds with coindex at most $3$ at a very…

In the note we study the multipoint Seshadri constants of $\mathcal{O}_{\mathbb{P}^{2}_{\mathbb{C}}}(1)$ centered at singular loci of certain curve arrangements in the complex projective plane. Our first aim is to show that the values of…