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Kavli IPMU Komaba Seminar
過去の記録 ～06/08｜次回の予定｜今後の予定 06/09～
| 開催情報 | 月曜日 16:30～18:00 数理科学研究科棟(駒場) 002号室 |
|---|---|
| 担当者 | 河野 俊丈 |
2012年06月08日(金)
16:30-18:00 数理科学研究科棟(駒場) 002号室
Bong Lian 氏 (Brandeis University)
Period Integrals and Tautological Systems (ENGLISH)
Bong Lian 氏 (Brandeis University)
Period Integrals and Tautological Systems (ENGLISH)
[ 講演概要 ]
We develop a global Poincar\\'e residue formula to study
period integrals of families of complex manifolds. For any compact
complex manifold X equipped with a linear system V∗ of
generically smooth CY hypersurfaces, the formula expresses period
integrals in terms of a canonical global meromorphic top form on X.
Two important ingredients of this construction are the notion of a CY
principal bundle, and a classification of such rank one bundles.
We also generalize the construction to CY and general type complete
intersections. When X is an algebraic manifold having a sufficiently
large automorphism group G and V∗ is a linear representation of
G, we construct a holonomic D-module that governs the period
integrals. The construction is based in part on the theory of
tautological systems we have developed earlier. The approach allows us
to explicitly describe a Picard-Fuchs type system for complete
intersection varieties of general types, as well as CY, in any Fano
variety, and in a homogeneous space in particular. In addition, the
approach provides a new perspective of old examples such as CY
complete intersections in a toric variety or partial flag variety. The
talk is based on recent joint work with R. Song and S.T. Yau.
We develop a global Poincar\\'e residue formula to study
period integrals of families of complex manifolds. For any compact
complex manifold X equipped with a linear system V∗ of
generically smooth CY hypersurfaces, the formula expresses period
integrals in terms of a canonical global meromorphic top form on X.
Two important ingredients of this construction are the notion of a CY
principal bundle, and a classification of such rank one bundles.
We also generalize the construction to CY and general type complete
intersections. When X is an algebraic manifold having a sufficiently
large automorphism group G and V∗ is a linear representation of
G, we construct a holonomic D-module that governs the period
integrals. The construction is based in part on the theory of
tautological systems we have developed earlier. The approach allows us
to explicitly describe a Picard-Fuchs type system for complete
intersection varieties of general types, as well as CY, in any Fano
variety, and in a homogeneous space in particular. In addition, the
approach provides a new perspective of old examples such as CY
complete intersections in a toric variety or partial flag variety. The
talk is based on recent joint work with R. Song and S.T. Yau.
