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Period Domains and Mumford-Tate Domains

Mark Green, Phillip Griffiths, and Matt Kerr

in Mumford-Tate Groups and Domains: Their Geometry and Arithmetic (AM-183)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691154244
eISBN:
9781400842735
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691154244.003.0003
Subject:
Mathematics, Analysis

This chapter provides an introduction to the basic definitions of period domains and their compact duals as well as the canonical exterior differential system on them. The period domain D is ... More


Arithmetic Aspects of Mumford-Tate Domains

Mark Green, Phillip Griffiths, and Matt Kerr

in Mumford-Tate Groups and Domains: Their Geometry and Arithmetic (AM-183)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691154244
eISBN:
9781400842735
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691154244.003.0007
Subject:
Mathematics, Analysis

This chapter describes the arithmetic aspects of Mumford-Tate domains and Noether-Lefschetz loci. It first clarifies a few points concerning the structure and construction of Mumford-Tate domains ... More


Classification of Mumford-Tate Subdomains

Mark Green, Phillip Griffiths, and Matt Kerr

in Mumford-Tate Groups and Domains: Their Geometry and Arithmetic (AM-183)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691154244
eISBN:
9781400842735
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691154244.003.0008
Subject:
Mathematics, Analysis

This chapter develops an algorithm for determining all Mumford-Tate subdomains of a given period domain. The result is applied to the classification of all complex multiplication Hodge structures (CM ... More


The Mumford-Tate Group of a Variation of Hodge Structure

Mark Green, Phillip Griffiths, and Matt Kerr

in Mumford-Tate Groups and Domains: Their Geometry and Arithmetic (AM-183)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691154244
eISBN:
9781400842735
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691154244.003.0004
Subject:
Mathematics, Analysis

This chapter deals with the Mumford-Tate group of a variation of Hodge structure (VHS). It begins by presenting a definition of VHS, which consists of a connected complex manifold and a locally ... More


Arithmetic of Period Maps of Geometric Origin

Mark Green, Phillip Griffiths, and Matt Kerr

in Mumford-Tate Groups and Domains: Their Geometry and Arithmetic (AM-183)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691154244
eISBN:
9781400842735
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691154244.003.0009
Subject:
Mathematics, Analysis

This chapter considers some arithmetic aspects of period maps with a geometric origin. It focuses on the situation Φ‎ : S(ℂ) → Γ‎\D, where S parametrizes a family X → S of smooth, projective ... More


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