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L. Katzarkov: “Gaps, Spectra, and Applications”

September 22, 2010, 11:13 am

Here are my notes from Katzarkov’s talk in Bonn:

Katzarkov_Bonn_Sep_2010

Summary:

  • Clemens-Griffiths showed that the 3-dimensional cubic is not rational by showing that its intermediate Jacobian is not the Jacobian of a curve; we suggest analogs of this.
  • Homological Mirror Symmetry and the perverse sheaf of vanishing cycles
  • detecting rationality via monodromy properties on the LG mirror (Gross-Katzarkov, Pryzalkowski, Golyshev)
  • spectra of triangulated categories; examples
  • Theorem: X is rational of dimension n implies that the spectrum of D^b(X) has no gaps of size greaeter than n-2
  • the outlook for 4-dimensional cubics
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