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SUMMARY:Berkovich approach to degenerations of hyper-Kähler varieties - E
 nrica Mazzon\, Imperial College
DTSTART:20181017T131500Z
DTEND:20181017T141500Z
UID:TALK112993@talks.cam.ac.uk
CONTACT:Roberto Svaldi
DESCRIPTION:To a degeneration of varieties\, we can associate the dual int
 ersection complex\, a topological space that encodes the combinatoric of t
 he central fiber and reflects the geometry of the generic fiber. In this t
 alk I will show how the techniques of Berkovich geometry give an insight i
 n the study of the dual complexes. In this way\, we are able to determine 
 the homeomorphism type of the dual complex of some degenerations of hyper-
 Kähler varieties. The results are in accordance with the predictions of m
 irror symmetry\, and the recent work about the rational homology of dual c
 omplexes of degenerations of hyper-Kähler varieties\, due to Kollár\, La
 za\, Saccà and Voisin. This is joint work with Morgan Brown.
LOCATION:CMS MR13
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