Variations of Hodge structure and orbits in flag varieties

Period domains, the classifying spaces for (pure, polarized) Hodge structures, and more generally Mumford–Tate domains, arise as open GR-orbits in flag varieties G/P. We investigate Hodge-theoretic aspects of the geometry and representation theory associated with these flag varieties. In particular,...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2017-07, Vol.315, p.27-87
Main Authors: Kerr, Matt, Robles, Colleen
Format: Article
Language:English
Subjects:
Boundary component
Mumford–Tate domain
Schubert variety
Variation of Hodge structure
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Summary:Period domains, the classifying spaces for (pure, polarized) Hodge structures, and more generally Mumford–Tate domains, arise as open GR-orbits in flag varieties G/P. We investigate Hodge-theoretic aspects of the geometry and representation theory associated with these flag varieties. In particular, we relate the Griffiths–Yukawa coupling to the variety of lines on G/P (under a minimal homogeneous embedding), construct a large class of polarized GR-orbits in G/P, and compute the associated Hodge-theoretic boundary components. An emphasis is placed throughout on adjoint flag varieties and the corresponding families of Hodge structures of levels two and four.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2017.05.013