Publication Date

1995

Journal or Book Title

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY

Abstract

Let S be a nonsingular complex algebraic variety and V a polarized variation of Hodge structure of weight 2p with polarization form Q. Given an integer K, let S(K) be the space of pairs (s, u) with s ∈ S, u ∈ Vs integral of type (p, p), and Q(u, u) ≤ K. We show in Theorem 1.1 that S(K) is an algebraic variety, finite over S. When V is the local system H2p (Xs, Z)/torsion associated with a family of nonsingular projective varieties parametrized by S, the result implies that the locus where a given integral class of type (p, p) remains of type (p, p) is algebraic.

Comments

This is the pre-published version harvested from ArXiv. The published version is located at http://www.jstor.org/stable/2152824

Pages

483-506

Volume

8

Issue

2

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