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    Mori Dream Spaces as fine moduli of quiver representations - Alastair Craw

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    Date: Thursday 1st November 2012
    Speaker: Alastair Craw (Glasgow)
    Title: Mori Dream Spaces as fine moduli of quiver representations

    Abstract: Mori Dream Spaces provide a relatively large class of examples in algebraic geometry that nevertheless exhibit many beautiful properties, the most obvious being that all operations of Mori Theory can be carried out by variation of GIT quotients. In particular, every Mori Dream Space can be constructed as a GIT quotient in a natural (though not canonical) way. In this talk I will introduce alternative GIT constructions using noncommutative algebra. As an application, we refine a result of Bergman-Proudfoot by showing that del Pezzo surfaces can be reconstructed from a tilting bundle.

    http://www.maths.ed.ac.uk/cheltsov/seminar/