Related papers: A note on multiple Seshadri constants on surfaces

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…

Based on the theory of an infinitesimal Newton-Okounkov body, we extend the results of Lazarsfeld-Pareschi-Popa on abelian surfaces. Moreover, we show that the higher syzygies of $(X,L)$ are completely determined by its Seshadri constant…

In this note, we continue the study of Seshadri constants on blow-ups of Hirzebruch surfaces initiated in arXiv:2312.14555. Now we consider blow-ups of ruled surfaces more generally. We propose a conjecture for classifying all the negative…

One of Demailly's characterizations of Seshadri constants on ample line bundles works with Lelong numbers of certain positive singular hermitian metrics. In this note sections of multiples of the line bundle are used to produce such metrics…

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…

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 give a lower bound of the $\delta$-invariants of ample line bundles in terms of Seshadri constants. As applications, we prove the uniform K-stability of infinitely many families of Fano hypersurfaces of arbitrarily large index, as well…

Let X be a projective variety of dimension n and L be a nef divisor on X. Denote by e_d(r;X,L) the d-dimensional Seshadri constant of r very general points in X. We prove that e_d(rs;X,L) >= e_d(r;X,L)e_d(s;P^n,O_{P^n}(1)).

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…

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…

In this paper, we study a relation between Seshadri constants and degrees of defining polynomials. In particular, we compute the Seshadri constants on Fano varieties obtained as complete intersections in rational homogeneous spaces of…

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…

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 $1/d$…

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…

Working over the complex field and formalizing and sharpening approaches introduced by several authors, we give a method for verifying when a divisor on a blow up of P^2 at general points is nef. The method is useful both theoretically and…

We study families of curves covering a projective surface and give lower bounds on the self-intersection of the members of such families, improving results of Ein-Lazarsfeld and Xu. We apply the obtained inequalities to get new insights on…

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…

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…

We establish an improvement of Philippon's zero estimates primarily in the multiplicity setting. The improvement is made possible by a more geometric approach and in particular the use of Seshadri constants.

The main goal of this paper is to present a new algorithm bounding the regularity and ``alpha'' (the lowest degree of existing hypersurface) of a linear system of hypersurfaces (in $\mathbb P^n$) passing through multiple points in general…