Variations of Hodge structure and orbits in flag varieties

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Kerr, M; Robles, C

Published Date

  • July 31, 2017

Published In

Volume / Issue

  • 315 /

Start / End Page

  • 27 - 87

Electronic International Standard Serial Number (EISSN)

  • 1090-2082

International Standard Serial Number (ISSN)

  • 0001-8708

Digital Object Identifier (DOI)

  • 10.1016/j.aim.2017.05.013

Citation Source

  • Scopus