Symplectic Geometry Seminar

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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


date speaker title host(s)
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

Abstracts

Ruifang Song The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties

Abstract

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.

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