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DTSTAMP:20230530T070437Z
UID:1679572800@ist.ac.at
DTSTART:20230323T130000
DTEND:20230323T150000
DESCRIPTION:Speaker: Justin Sawon\nhosted by Tamas Hausel\nAbstract: The ge
neralized Kummer variety K_n of an abelian surface A is the fibre of the n
atural map Hilb^{n+1}A->Sym^{n+1}A->A. Debarre described a Lagrangian fibr
ation on K_n whose fibres are the kernels of JacC->A\, where C are curves
in a fixed linear system in A. A different (isotrivial) Lagrangian fibrati
on on K_n arises when A is the product of elliptic curves. In this talk we
consider the dual Lagrangian fibrations. The dual of the Debarre system i
s constructed in a similar way to the duality between SL- and PGL-Hitchin
systems described by Hausel and Thaddeus\, and in a few cases we are able
to verify topological mirror symmetry'\, i.e.\, equality of (stringy) Hodg
e numbers of the Debarre fibration and its dual. The dual of the isotrivia
l fibration is easier to describe and we can verify topological mirror sym
metry in many more cases. Finally\, we speculate on how to enhance this to
homological mirror symmetry'.
LOCATION:Heinzel Seminar Room (I21.EG.101)\, Office Building West\, ISTA\,
ISTA
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:Justin Sawon: Mirror symmetry for generalized Kummer varieties
URL:https://talks-calendar.ista.ac.at/events/4077
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