Related papers: Seshadri constants of parabolic vector bundles

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…

Let $X^n_{r,s}$ denote the blow-up of $\mathbb{P}^n$ along $r$ general lines and $s$ general points. In this paper, we focus on $l$-very ample line bundles on $X^n_{0,s}$ and investigate their Seshadri constants with some restrictions on…

We prove that certain vector bundles over surfaces are ample if they are so when restricted to divisors, certain numerical criteria hold, and they are semistable (with respect to $\det(E)$). This result is a higher-rank version of a theorem…

In the present note, we focus on certain properties of special curves that might be used in the theory of multi-point Seshadri constants for ample line bundles on the complex projective plane. In particular, we provide three…

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…

We introduce higher-order variants of the Frobenius-Seshadri constant due to Musta\c{t}\u{a} and Schwede, which are defined for ample line bundles in positive characteristic. These constants are used to show that Demailly's criterion for…

In this paper we explore the connection between Seshadri constants and the generation of jets. It is well-known that one way to view Seshadri constants is to consider them as measuring the rate of growth of the number of jets that multiples…

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…

Let $\pi: X_r \rightarrow \mathbb P^2$ be a blow up of $\mathbb P^2$ at $r$ distinct points $p_1,p_2,\dots, p_r$. We study lower bounds for Seshadri constants of ample line bundles on $X_r$. First, we consider the case when the points lie…

Let $M$ be the moduli space of generalized parabolic bundles (GPBs) of rank $r$ and degree $d$ on a smooth curve $X$. Let $M_{\bar L}$ be the closure of its subset consisting of GPBs with fixed determinant ${\bar L}$. We define a moduli…

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}…

Given a smooth complex projective variety $X$ and an ample line bundle $L$ on $X$. Fix a point $x\in X$. We consider the question, are there conditions which guarantee the maxima of the Seshadri constant of $L$ at $x$, i.e $\eps(L,x)=\root…

Let $X$ be a normal projective variety equipped with an action of a semisimple algebraic group $G$, and assume that $X$ contains a unique closed orbit. Let $B$ be a Borel subgroup of $G$ and let $E$ be a $B$-equivariant vector bundle on…

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 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…

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…

We construct projectivization of a parabolic vector bundle and a tautological line bundle over it. It is shown that a parabolic vector bundle is ample if and only if the tautological line bundle is ample. This allows us to generalize the…

Algebraic parabolic bundles on smooth projective curves over algebraically closed field of positive characteristic is defined. It is shown that the category of algebraic parabolic bundles is equivalent to the category of orbifold bundles…

For every set of parabolic weights, we construct a Harder-Narasimhan stratification for the moduli stack of parabolic vector bundles on a curve. It is based on the notion of parabolic slope, introduced by Mehta and Seshadri. We also prove…

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…