6 Citations
Some results on Seshadri constants on surfaces of general type
- Mathematics
- 2019
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 Bauer and Szemberg (Manuscripta Math 126(2):167–175,…
Extended Okounkov bodies and multi-point Seshadri constants
- Mathematics
- 2017
Based on the work of Okounkov, Lazarsfeld-Mustata and Kaveh-Khovanskii independently associated a convex body, called the Okounkov body, to a big divisor on a smooth projective variety with respect…
Rationality of Seshadri constants on general blow ups of $\mathbb{P}^2$
- Mathematics
- 2019
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…
Non-existence of negative curves
- Mathematics
- 2021
Let X be a projective toric surface of Picard number one blown up at a general point. We bring an infinite family of examples of such Xwhose Kleiman-Mori cone of curves is not closed: there is no…
Irrational nef rays at the boundary of the Mori cone for very general blowups of the plane
- Mathematics
- 2022
In this paper we develop a technique for discovering (non-effective) irrational rays at the boundary of the Mori cone for linear systems on a general blowup of the plane, and give examples of such…
References
SHOWING 1-10 OF 11 REFERENCES
Restrictions on Seshadri constants on surfaces
- Mathematics
- 2017
Starting with the pioneering work of Ein and Lazarsfeld [9] restrictions on values of Seshadri constants on algebraic surfaces have been studied by many authors [2,5,10,12,18,20,22,24]. In the…
Multi-point Seshadri constants on ruled surfaces
- Mathematics
- 2016
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…
Seshadri constants and very ample divisors on algebraic surfaces
- Mathematics
- 2001
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…
Ample Line Bundles on Blown Up Surfaces
- Mathematics
- 1994
Given a smooth complex projective surface $S$ and an ample divisor $H$ on $S$, consider the blow up of $S$ along $k$ points in general position. Let $H'$ be the pullback of $H$ and $E_1,..., E_k$ be…
Rationality of Seshadri constants and the Segre–Harbourne–Gimigliano–Hirschowitz conjecture
- Mathematics
- 2016
Ample line bundles on blown up surfaces
- Mathematics
- 1996
ample ? We show that the condition L > 0, which clearly is necessary, is also sufficient provided the integer n is at least 3. Note that the answer to this question has been unknown even in the case…
Divisors on the blow-up of the projective plane
- Mathematics
- 1995
We study the ampleness of divisors on the blow-up of the complex projective plane atk generic points, and give an affirmative answer to a question of Fujita.