# On a family of negative curves

@article{GonzalezAnaya2019OnAF, title={On a family of negative curves}, author={Javier Gonz'alez-Anaya and Jos'e Luis Gonz'alez and Kalle Karu The University of British Columbia and The University of California at Riverside}, journal={Journal of Pure and Applied Algebra}, year={2019} }

## 8 Citations

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…

Negative curves in blowups of weighted projective planes

- Mathematics
- 2020

We study the Mori dream space property for blowups at a general point of weighted projective planes or, more generally, of toric surfaces with Picard number one. Such a variety is a Mori dream space…

Curves generating extremal rays in blowups of weighted projective planes

- MathematicsJournal of the London Mathematical Society
- 2020

We consider blowups at a general point of weighted projective planes and, more generally, of toric surfaces with Picard number 1. We give a unifying construction of negative curves on these blowups…

On intrinsic negative curves

- Mathematics
- 2021

Let K be an algebraically closed field of characteristic 0. A curve of (K∗)2 arising from a Laurent polynomial in two variables is intrinsic negative if its tropical compactification has negative…

Mori Dream Spaces and blow-ups of weighted projective spaces

- MathematicsJournal of Pure and Applied Algebra
- 2019

Symbolic Rees Algebras

- MathematicsCommutative Algebra
- 2021

We survey old and new approaches to the study of symbolic powers of ideals. Our focus is on the symbolic Rees algebra of an ideal, viewed both as a tool to investigate its symbolic powers and as a…

The geography of negative curves

- Mathematics
- 2021

We study the Mori Dream Space (MDS) property for blowups of weighted projective planes at a general point and, more generally, blowups of toric surfaces defined by a rational plane triangle. The…

## References

SHOWING 1-10 OF 13 REFERENCES

Some non-finitely generated Cox rings

- MathematicsCompositio Mathematica
- 2015

We give a large family of weighted projective planes, blown up at a smooth point, that do not have finitely generated Cox rings. We then use the method of Castravet and Tevelev to prove that the…

On blowing up the weighted projective plane

- MathematicsMathematische Zeitschrift
- 2018

We investigate the blow-up of a weighted projective plane at a general point. We provide criteria and algorithms for testing if the result is a Mori dream surface and we compute the Cox ring in…

Infinitely Generated Symbolic Rees Rings of Space Monomial Curves Having Negative Curves

- MathematicsMichigan Mathematical Journal
- 2019

In this paper, we shall study finite generation of symbolic Rees rings of the defining ideal ${\frak p}$ of the space monomial curve $(t^a, t^b, t^c)$ for pairwise coprime integers $a$, $b$, $c$.…

On the finite generation of symbolic blow-ups

- Mathematics
- 1982

"symbolic blow-up", (~ P(n)=S a Noetherian ring? If S is Noetherian and dim n 0 RIP=l, Cowsik observed that P must be a set-theoretic complete intersection. If R is not regular, there is no hope in…

New Examples and Non-examples of Mori Dream Spaces when Blowing up Toric Surfaces

- Mathematics
- 2017

We study the question of whether the blow-ups of toric surfaces of Picard number one at the identity point of the torus are Mori Dream Spaces. For some of these toric surfaces, the question whether…

Mori dream spaces and GIT.

- Mathematics
- 2000

The main goal of this paper is to study varieties with the best possible Mori theoretic properties (measured by the existence of a certain decomposition of the cone of effective divisors). We call…

Introduction to toric varieties

- Mathematics
- 2004

The course given during the School and Workshop “The Geometry and Topology of Singularities”, 8-26 January 2007, Cuernavaca, Mexico is based on a previous course given during the 23o Coloquio…

Symbolic algebras of monomial primes.

- Mathematics
- 1991

Determination of when symbolic algebras are finitely generated is central to commutative algebra and algebraic geometry. One of the simplest non-trivial classes of examples, which are not divisorial,…

Cox Rings

- 2015

Introduction to toric varieties, volume 131 of Annals of Mathematics Studies

- The William H. Roever Lectures in Geometry
- 1993