Spherical blow-ups of Grassmannians and Mori Dream Spaces
Abstract
In this paper we classify weak Fano varieties that can be obtained by blowing-up general points in prime Fano varieties. We also classify spherical blow-ups of Grassmannians in general points, and we compute their effective cone. These blow-ups are, in particular, Mori dream spaces. Furthermore, we compute the stable base locus decomposition of the blow-up of a Grassmannian in one point, and we show how it is determined by linear systems of hyperplanes containing the osculating spaces of the Grassmannian at the blown-up point, and by the rational normal curves in the Grassmannian passing through the blown-up point.
Keywords
Cite
@article{arxiv.1705.04972,
title = {Spherical blow-ups of Grassmannians and Mori Dream Spaces},
author = {Alex Massarenti and Rick Rischter},
journal= {arXiv preprint arXiv:1705.04972},
year = {2017}
}
Comments
23 pages. Exposition improved and corrected a statement on the stable base locus decomposition in Theorem 1.3 thanks to the comments of the referee