Mathematics > Algebraic Geometry
[Submitted on 24 May 2011 (v1), last revised 23 Apr 2019 (this version, v7)]
Title:Period Integrals of CY and General Type Complete Intersections
View PDFAbstract:We develop a global Poincaré 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 our construction are the notion of a CY principal bundle, and a classification of such rank one bundles. We also generalize our 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 in the paper \cite{LSY1}, joint with R. Song. 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.
Submission history
From: Bong H. Lian [view email][v1] Tue, 24 May 2011 19:55:35 UTC (40 KB)
[v2] Thu, 16 Jun 2011 14:59:17 UTC (40 KB)
[v3] Mon, 26 Mar 2012 12:23:57 UTC (41 KB)
[v4] Tue, 15 May 2012 20:27:34 UTC (41 KB)
[v5] Fri, 2 Aug 2013 18:27:20 UTC (41 KB)
[v6] Mon, 5 Aug 2013 18:23:44 UTC (41 KB)
[v7] Tue, 23 Apr 2019 01:46:01 UTC (46 KB)
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