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Oberseminar WiSe 12/13 Zusammenfassung des Vortrags von Johannes Nicaise (University of Leuven)

The Kontsevich-Soibelman skeleteon of a degeneration of Calabi-Yau varieties

I will explain the construction of the skeleton that was defined by Kontsevich and Soibelman to give a non-archimedean interpretation of Mirror Symmetry. This skeleton is a simplicial space embedded in the Berkovich space associated to a one-parameter degeneration of complex Calabi-Yau varieties. Using suitable variants of vanishing theorems in birational geometry, I will prove that the skeleton is always connected. This is joint work with Mircea Mustata (Michigan).