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Period Domains and Mumford-Tate Domains
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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 comprised of a set of polarized Hodge structures. The natural symmetry group acting on D is the group G(ℝ) of real points of the ℚ-algebraic group G = Aut(V,Q). Elementary linear algebra shows that G(ℝ) operates transitively on D. The chapter also discusses Mumford-Tate domains and their compact duals as well as the Noether-Lefschetz locus in period domains. The basic properties of Mumford-Tate domains are established in several places.
Princeton University Press
Title: Period Domains and Mumford-Tate Domains
Description:
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 comprised of a set of polarized Hodge structures.
The natural symmetry group acting on D is the group G(ℝ) of real points of the ℚ-algebraic group G = Aut(V,Q).
Elementary linear algebra shows that G(ℝ) operates transitively on D.
The chapter also discusses Mumford-Tate domains and their compact duals as well as the Noether-Lefschetz locus in period domains.
The basic properties of Mumford-Tate domains are established in several places.
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