## 9 Citations

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…

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…

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…

Mori dreamness of blowups of weighted projective planes

- Mathematics
- 2021

We consider the blowup X(a, b, c) of a weighted projective space $${\mathbb {P}}(a,b,c)$$
at a general nonsingular point. We give a sufficient condition for a curve to be a negative curve on X(a, b,…

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…

Equations of negative curves of blow-ups of Ehrhart rings of rational convex polygons

- MathematicsJournal of Algebra
- 2021

Some necessary and sufficient condition for finite generation of symbolic Rees rings

- Mathematics
- 2022

. Consider the blow-up Y of a weighted projective plane at a point in the open orbit over a ﬁeld of characteristic 0. We assume that there exists a curve C on Y such that C 2 < 0 and C.E = 1, where E…

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 18 REFERENCES

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…

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…

M0;n IS NOT A MORI DREAM SPACE

- Mathematics
- 2015

Building on the work of Goto, Nishida, and Watanabe on symbolic Rees algebras of monomial primes, we prove that the moduli space of stable rational curves with n punctures is not a Mori dream space…

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…

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…

$\overline{M}_{0,n}$ is not a Mori Dream Space

- Mathematics
- 2013

Building on the work of Goto, Nishida and Watanabe on symbolic Rees algebras of monomial primes, we prove that the moduli space of stable rational curves with n punctures is not a Mori Dream Space…

On finite generation of symbolic Rees rings of space monomial curves and existence of negative curves

- Mathematics
- 2008

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 $a$, $b$, $c$.…

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,…