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arXiv · 1705.04972

Spherical blow-ups of Grassmannians and Mori Dream Spaces

Alex Massarenti·Rick Rischter
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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.

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Alex Massarenti, Rick Rischter. 2017-05-14. Spherical blow-ups of Grassmannians and Mori Dream Spaces. https://doi.org/10.1016/j.jalgebra.2017.09.037

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