Symplectic Geometry Seminar: Difference between revisions
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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. | 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 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. | ||
In general, | |||
==Past Semesters == | ==Past Semesters == | ||
*[[ Spring 2011 Symplectic Geometry Seminar]] | *[[ Spring 2011 Symplectic Geometry Seminar]] | ||
Revision as of 16:05, 15 September 2011
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. 28th | 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.