On the closure of the positive Hodge locus

Abstract

Given a variation of Hodge structures on a quasi-projective base $S$, whose generic Mumford-Tate group is non-product, we prove that the (countable) union of positive components of the Hodge locus is either an algebraic subvariety of $S$, or is Zariski-dense in $S$.

Cited by in corpus (2)

• Effective transcendental Zilber-Pink for variations of Hodge structures
• On the geometric André-Oort conjecture for variations of Hodge structures