- Title : Mirror symmetry
for Fano threefolds: toric degenerations,
uniqueness and
non-uniquenes
- 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 Landau--Ginzburg models. Such
polynomial is not unique for given Fano variety. Conjecturally all
``good'' weak Landau--Ginzburg 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 Landau--Ginzburg models. Finally
we discuss geometry of toric Landau--Ginzburg models and prove that they, from some point of view, are unique.
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