Kuga-Satake construction for K3 surfaces near the boundary of
 moduli  -- Valery Alexeev, March 10, 2010                                                       

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Mumford observed that the Torelli map from Mg (moduli of
curves) to Ag (moduli of principally polarized abelian
varieties), sending a smooth curve of genus g to its Jacobian,
can be extended to a morphism between compactifications, the
Deligne-Mumford compactification of Mg and a particular
toroidal compactification of Ag. Namikawa showed how to make
this construction geometric, and I explained how to make it
functorial.
                  
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 I will show that in several examples the Kuga-Satake
 construction, sending a K3 surface to an abelian variety,
 behaves in a similar way near the boundary of the respective
 moduli spaces.