Article ID Journal Published Year Pages File Type
5778615 Advances in Mathematics 2017 61 Pages PDF
Abstract
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.
Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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