Jump to ContentJump to Main Navigation
Hodge Theory (MN-49)$
Users without a subscription are not able to see the full content.

Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, and Lê Dung Tráng

Print publication date: 2014

Print ISBN-13: 9780691161341

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691161341.001.0001

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2018. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in HSO for personal use (for details see www.princeton.universitypressscholarship.com/page/privacy-policy).date: 19 October 2018

Period Domains and Period Mappings

Period Domains and Period Mappings

(p.217) Chapter Four Period Domains and Period Mappings
Hodge Theory (MN-49)

James Carlson

, Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, Lê Dũng Tráng
Princeton University Press

This chapter seeks to develop a working understanding of the notions of period domain and period mapping, as well as familiarity with basic examples thereof. It first reviews the notion of a polarized Hodge structure H of weight n over the integers, for which the motivating example is the primitive cohomology in dimension n of a projective algebraic manifold of the same dimension. Next, the chapter presents lectures on period domains and monodromy, as well as elliptic curves. Hereafter, the chapter provides an example of period mappings, before considering Hodge structures of weight. After expounding on Poincaré residues, this chapter establishes some properties of the period mapping for hypersurfaces and the Jacobian ideal and the local Torelli theorem. Finally, the chapter studies the distance-decreasing properties and integral manifolds of the horizontal distribution.

Keywords:   period domains, period mappings, monodromy, elliptic curves, Hodge structures, Poincaré residues, hypersurfaces, Jacobian ideal, Torelli theorem, horizontal distribution

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.