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Title:
The essential skeleton of a degeneration of algebraic varieties
Speaker:
Abstract:
I will survey my joint work with Mircea Mustata and Chenyang Xu on the relations between the topology of Berkovich spaces and degenerations of algebraic varieties. Studying non-archimedean weight functions attached to pluricanonical forms, we defined the essential skeleton of the Berkovich analytification of a smooth and proper variety X over the field of complex Laurent series. This generalizes a construction of Kontsevich and Soibelman for Calabi-Yau varieties. It turns out that the essential skeleton can be canonically identified with the dual complex of the special fiber of any minimal dlt-model of the degeneration; then it follows from work of Berkovich and de Fernex-Kollár-Xu that the essential skeleton is a strong deformation retract of the analytification of X. If time permits, I will also present an application to the theory of Igusa zeta functions in number theory (proof of Veys's conjecture on poles of maximal order).
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