The locus of Hodge classes in an admissible variation of mixed Hodge structure
نویسندگان
چکیده
Article history: Received 29 March 2010 Accepted 8 April 2010 Presented by Pierre Deligne We generalize the theorem of E. Cattani, P. Deligne, and A. Kaplan to admissible variations of mixed Hodge structure. © 2010 Académie des sciences. Published by Elsevier Masson SAS. All rights reserved. r é s u m é On généralise le théorème de E. Cattani, P. Deligne, et A. Kaplan aux variations de structure de Hodge mixtes admissibles. © 2010 Académie des sciences. Published by Elsevier Masson SAS. All rights reserved.
منابع مشابه
Fields of Definition of Hodge Loci
We show that an irreducible component of the Hodge locus of a polarizable variation of Hodge structure of weight 0 on a smooth complex variety X is defined over an algebraically closed subfield k of finite transcendence degree if X is defined over k and the component contains a k-rational point. We also prove a similar assertion for the Hodge locus inside the Hodge bundle if the Hodge bundle to...
متن کاملThe Extended Locus of Hodge Classes
We introduce an “extended locus of Hodge classes” that also takes into account integral classes that become Hodge classes “in the limit”. More precisely, given a polarized variation of integral Hodge structure of weight zero on a Zariski-open subset of a complex manifold, we construct a canonical analytic space that parametrizes limits of integral classes; the extended locus of Hodge classes is...
متن کاملComplex analytic Néron models for arbitrary families of intermediate Jacobians
Given a family of intermediate Jacobians (for a polarizable variation of integral Hodge structure of odd weight) on a Zariski-open subset of a complex manifold, we construct an analytic space that naturally extends the family. Its two main properties are: (a) the horizontal and holomorphic sections are precisely the admissible normal functions without singularities; (b) the graph of any admissi...
متن کاملCharacteristic classes of mixed Hodge modules
This paper is an extended version of an expository talk given at the workshop “Topology of Stratified Spaces” at MSRI in September 2008. It gives an introduction and overview about recent developments on the interaction of the theories of characteristic classes and mixed Hodge theory for singular spaces in the complex algebraic context. It uses M. Saito’s deep theory of mixed Hodge modules as a...
متن کاملSingularities of Variations of Mixed Hodge Structure
We prove that a variation of graded-polarizable mixed Hodge structure over a punctured disk with unipotent monodromy, has a limiting mixed Hodge structure at the puncture (i.e., it is admissible in the sense of [SZ]) which splits over R, if and only if certain grading of the complexified weight filtration, depending smoothly on the Hodge filtration, has a real limit at the puncture. In particul...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010