Constructing non-Mori Dream Spaces from negative curves
Algebraic Geometry
2018-10-02 v1 Commutative Algebra
Abstract
We study blowups of weighted projective planes at a general point, and more generally blowups of toric surfaces of Picard number one. Based on the positive characteristic methods of Kurano and Nishida, we give a general method for constructing examples of Mori Dream Spaces and non-Mori Dream Spaces among such blowups. Compared to previous constructions, this method uses the geometric properties of the varieties and applies to a number of cases. We use it to fully classify the examples coming from two families of negative curves.
Keywords
Cite
@article{arxiv.1810.00508,
title = {Constructing non-Mori Dream Spaces from negative curves},
author = {Javier González-Anaya and José Luis González and Kalle Karu},
journal= {arXiv preprint arXiv:1810.00508},
year = {2018}
}
Comments
18 pages, 6 figures