|Speaker:||Sergey Galkin (IPMU)|
|Title:||Mirror symmetries of P2 enumerated by Markov triplets.|
|Date (JST):||Tue, Jan 19, 2010, 13:15 - 14:45|
|Place:||Balcony B on the 5th floor of the IPMU new building|
Triplets of integer numbers (x,y,z) satisfying Markov's equation
x2 + y2 + z2 = 3 xyz
are in charge of two numerologies for the projective plane P2:
these numbers are the ranks of exceptional bundles
and their squares are the weights of Prokhorov-Hacking's degenerations
of the plane to weighted projective plane P(x2,y2,z2).
Batyrev's ansatz states that given a (good) toric degeneration of variety X
one may construct a Landau-Ginzburg model mirror dual to X as a
Laurent polynomial with the Newton polytope being the fan polytope of
I'll show this ansatz holds in the situation of Prokhorov-Hacking's
and relate the polynomials constructed from different degenerations by
birational symplectomorphic mutations.