The homological projective dual of Sym^2(P^n)
Joergen Rennemo (Imperial College) Seminar Algebraic Geometry (SAG)
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When 
Oct 23, 2014 from 10:30 am to 11:30 am 
Where  Bonn, HĂ¶rsaal MPI, Vivatsgasse 7 
Contact Name  Sachinidis 
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We produce semiorthogonal decompositions of the derived categories of complete intersections in Sym^2(P^n). These fit into Kuznetsov's theory of homological projective duality, which gives a description of the derived categories of all complete intersections in terms of the "homological projective dual" of Sym^2(P^n). An alternative approach to HP duality has recently been developed based on categories of matrix factorisations and VGIT. I will explain the necessary background for this method and show how it applies to our example. As an application of the HP duality statement, we reprove a theorem of Hosono and Takagi which says that a certain pair of nonbirational CalabiYau 3folds are derived equivalent.