26 citations · 91 across the 24 of their papers we have counts for
24 papers
Symbolic Rees algebras of space monomial primes of degree 5
Kazuhiko Kurano
Let K be a field of characteristic 0. Let P_K(5,103,169) be the defining ideal of the space monomial curve {(t^5,t^{103},t^{169})}. In this paper we shall prove that the symbolic R…
Infinitely generated symbolic Rees rings of positive characteristic
Kazuhiko Kurano
Let X be a toric variety over a field K determined by a triangle. Let Y be the blow-up at (1,1) in X. In this paper we give some criteria for finite generation of the Cox ring of Y…
Some necessary and sufficient condition for finite generation of symbolic Rees rings
Taro Inagawa, Kazuhiko Kurano
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…
Equations of negative curves of blow-ups of Ehrhart rings of rational convex polygons
Kazuhiko Kurano
Finite generation of the symbolic Rees ring of a space monomial prime ideal of a 3-dimensional weighted polynomial ring is a very interesting problem. Negative curves play importan…
Demazure construction for Z^n-graded Krull domains
Yusuke Arai, Ayaka Echizenya, Kazuhiko Kurano
For a Mori dream space X, the Cox ring Cox(X) is a Noetherian Z^n-graded normal domain for some n > 0. Let C(Cox(X)) be the cone (in R^n) which is spanned by the vectors a \in Z^n…
Infinitely generated symbolic Rees rings of space monomial curves having negative curves
Kazuhiko Kurano, Koji Nishida
In this paper, we shall study finite generation of symbolic Rees rings of the defining ideal of the space monomial curve for pairwise coprime integers…