# Rationality of Seshadri constants and the Segre–Harbourne–Gimigliano–Hirschowitz conjecture

@article{Dumnicki2016RationalityOS, title={Rationality of Seshadri constants and the Segre–Harbourne–Gimigliano–Hirschowitz conjecture}, author={Marcin Dumnicki and A. K{\"u}ronya and Catriona Maclean and Tomasz Szemberg}, journal={Advances in Mathematics}, year={2016}, volume={303}, pages={1162-1170} }

## 15 Citations

Seshadi constants via functions on Newton–Okounkov bodies

- Mathematics
- 2016

The aim of this note is to establish a somewhat surprising connection between functions on Newton–Okounkov bodies and Seshadri constants of line bundles on algebraic surfaces.

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…

Concave transforms of filtrations and rationality of Seshadri constants

- Mathematics
- 2019

We show that the subgraph of the concave transform of a multiplicative filtration on a section ring is the Newton--Okounkov body of a certain semigroup, and if the filtration is induced by a…

Geometric aspects of Newton-Okounkov bodies

- Mathematics
- 2017

This is a survey article on Newton-Okounkov bodies in projective geometry focusing on the relationship between positivity of divisors and Newton-Okounkov bodies.

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…

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,…

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…

A G ] 1 4 N ov 2 01 8 Multipoint Okounkov bodies

- Mathematics
- 2018

Starting from the data of a big line bundle L on a projective manifold X with a choice of N ≥ 1 different points on X we give a new construction of N Okounkov bodies that encodes important geometric…

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