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

@article{Kurano2008OnFG, title={On finite generation of symbolic Rees rings of space monomial curves and existence of negative curves}, author={Kazuhiko Kurano and Naoyuki Matsuoka}, journal={Journal of Algebra}, year={2008}, volume={322}, pages={3268-3290} }

## 18 Citations

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

- MathematicsJournal of Algebra
- 2021

Symbolic blowup algebras and invariants of certain monomial curves in an affine space

- Mathematics
- 2016

Abstract Let and be integers such that Let be the defining ideal of the monomial curve in parametrized by where for all In this paper, we describe the symbolic powers for all As a consequence, we…

Asymptotic regularity of powers of ideals of points in a weighted projective plane

- Mathematics
- 2011

In this paper we study the asymptotic behavior of the regularity of symbolic powers of ideals of points in a weighted projective plane. By a result of Cutkosky, Ein and Lazarsfeld, regularity of such…

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…

Multiplicities of Monomial Space Curves with Non-Noetherian Symbolic Blowups

- Mathematics
- 2015

We study the multiplicities of space monomial curves with non-Noetherian symbolic blowups. We extend the celebrated examples of Goto, Nishida, and Watanabe, as well as introduce a new family of…

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…

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…

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…

On curves with high multiplicity on P ( a , b , c ) for min ( a , b , c ) ≤ 4

- Mathematics
- 2021

On aweighted projective surfaceP(a, b, c)withmin(a, b, c) ≤ 4, we compute lower bounds for the e ective threshold of an ample divisor, in other words, the highest multiplicity a section of the…

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