Symplectic Geometry Seminar
Wednesday 3:30pm-4:30pm VV B139
- If you would like to talk in the seminar but have difficulty with adding information here, please contact Dongning Wang
|Sept. 21st||Ruifang Song||The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties|
|Sept. 28st||Ruifang Song||The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties(continued)|
|Oct. 5th||Dongning Wang||Seidel Representation for Symplectic Orbifolds|
Ruifang Song The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus has finite dimensional solution space assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. In particular, when X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which have played important roles in studying periods of Calabi-Yau hypersurfaces/complete intersections in toric varieties. In general, if X is a Fano variety, L is the anticanonical line bundle and G=Aut(X), this construction can be used to study the Picard-Fuchs system of Calabi-Yau hypersurfaces/complete intersections in X.