相关论文: Remarks on Seshadri constants

In this paper, we investigate the Seshadri constant $\varepsilon(X,T_X;p)$ of the tangent sheaf $T_X$ on a complete $\mathbb Q$-factorial toric variety $X$. We show that $\varepsilon(X,T_X;1)>0$ if and only if the following statement holds…

Let $X$ be a general hypersurface of degree $md$ in the weighted projective space with weights $1,1,1,m$ for some for $d\geq 2$ and $m\geq 3$. We prove that the Seshadri constant of the ample generator of the N\'eron-Severi space at a…

This paper studies the Seshadri constant of an ample line bundle at a very general point, seeking a very slight improvement on the result of Ein, Kuchle, and Lazarsfeld. The main point is that couting jets more carefully yields a better…

In analogy to the relation between symplectic packings and symplectic blow ups we show that multiple point Seshadri constants on projective complex surfaces can be calculated as the supremum of radii of multiple K\"ahler ball embeddings.

In this paper, we associate an invariant $\alpha_{x}(L)$ to an algebraic point $x$ on an algebraic variety $X$ with an ample line bundle $L$. The invariant $\alpha$ measures how well $x$ can be approximated by rational points on $X$, with…

Let $X$ be a smooth complex projective curve, and let $E$ be a vector bundle on $X$ which is not semistable. For a suitably chosen integer $r$, let $\text{Gr}(E)$ be the Grassmann bundle over $X$ that parametrizes the quotients of the…

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,…

We refine results of Hwang, Keum and Szemberg, Tutaj-Gasinska which relate local invariants - Seshadri constants - of ample line bundles on surfaces to the global geometry - fibration structure. We show that the same picture emerges when…

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…

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}…

In the paper we present an alternative approach to the boundedness of Seshadri constants (which measure the local positivity) of nef and big line bundles at a general point of a complex--projective variety. Our approach is based 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…

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…

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 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…

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…

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.

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…

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…

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…