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Mori Dream Spaces and Blowups of Weighted Projective Planes

Banff International Research Station for Mathematical Innovation and Discovery

Mori Dream Spaces were introduced by Hu and Keel as normal, Q-factorial projective varieties whose effective cone admits a nice decomposition. Mori's minimal model program can be run for every divisor on a Mori Dream Space. Recently there have been many studies on the question that for which integers a,b,c the blow-up of the weighted projective plane P(a,b,c) at a general point is a Mori Dream Space. In this talk, I will recall these recent work, and introduce a generalization of a result by González and Karu in 2014. Specifically, for some toric surfaces of Picard number one, whether the blow-up is a Mori Dream Space is equivalent to countably many planar interpolation problems. I will give new examples and non-examples of Mori Dream Spaces, along with a conjecture of more non-examples, by reducing these interpolation problems.

Mathematics; Algebraic geometry; Convex and discrete geometry

video/mp4

Author affiliation: Northeastern University

2017-11-08

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63566

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/