 Title : Mirror symmetry
for Fano threefolds: toric degenerations,
uniqueness and
nonuniquenes
 Speaker : Victor Przyjalkowskiy (Steklov Institute/ U. of Wien)  Date & Time : 27 June , 2012 (Wed) 14:00~15:00  Place : Math Science Building room 404  Abstract :
Mirror symmetry, from variations of Hodge structures
point of view, relates Fano varieties and particular Laurent polynomials  toric LandauGinzburg models. Such
polynomial is not unique for given Fano variety. Conjecturally all
``good'' weak LandauGinzburg models correspond to toric degenerations of Fano varieties. We
consider examples of such correspondence for Fano threefolds. In particular
we observe ways to prove that particular toric varieties are degenerations of
Rank 1 Fano threefolds. We reconstruct
some numerical invariants of Fano varieties from their toric LandauGinzburg models. Finally
we discuss geometry of toric LandauGinzburg models and prove that they, from some point of view, are unique.

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