A degenerate reason why trivial is not always good – Luigi Lunardon (Imperial College London)


Sala Seminari (Dip. Matematica).


A degenerate reason why trivial is not always good Abstract: In this talk, we focus on degeneration of low dimensional Calabi-Yau varieties.All the mysterious words in this abstract will be explained. It is not surprising that, while curves are easy to understand and we have some control on degenerations of surfaces, things get wild in dimension three. In particular, we see that a consequence of Kulikov classification is that, for K3 surfaces, trivial monodromy implies good reduction; however, we show thatthere is no analogous statement fordegenerations of a generic Calabi-Yau 3-fold. We recall the classical definition of degeneration and explain how to translate this in the language of algebraic geometry. After this warm-up, we explain what is Kulikov classification of generic fibres of semistable degenerations of K3 surfaces and we show an example of degenerating Calabi-Yau 3-folds with trivial monodromy that does not admit good reduction. Prerequisiti: Basic Algebraic Geometry (Canonical bundle, blow ups, fibre products, cohomology…) Sito web:http://people.dm.unipi.it/babygeometri/

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