Opposite filtrations, variations of Hodge structure, and Frobenius modules Chapter uri icon

abstract

  • Let X be a complex manifold. Then, an unpolarized complex variation of Hodge structure (E, ∇, F, Φ̄) over X consists of a flat, C∞ complex vector bundle (E, ∇) over X equipped with a decreasing Hodge filtration F and an increasing filtration Φ̄ such that(1.1)F is holomorphic with respect to ∇, and $$
    abla left({{F^{p}}}
    ight) subseteq {F^{{p - 1}}} otimes Omega _{X}^{1}$$;(1.2)Φ̄ is anti-holomorphic with respect to ∇, and $$
    abla left({{{\bar{Phi}}_{q}}}
    ight)subseteq {\bar{Phi}_{{q + 1}}} otimes overline {Omega _{X}^{1}} $$;(1.3)$$ E = {F^{p}} oplus {\bar{Phi }_{{p - 1}}}$$for each index p (i.e. F is opposite to Φ̄).

author list (cited authors)

  • Fernandez, J., & Pearlstein, G.

complete list of authors

  • Fernandez, Javier||Pearlstein, Gregory

editor list (cited editors)

  • Hertling, K., & Marcolli, M.

Book Title

  • Frobenius Manifolds

publication date

  • January 1, 2004 11:11 AM