| 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 |
| Abstract: |
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 the degeneration. I'll show this ansatz holds in the situation of Prokhorov-Hacking's degenerations, and relate the polynomials constructed from different degenerations by birational symplectomorphic mutations. |
| Contact: | Kondo |
