## 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.