Definability of mixed period maps

Abstract

We equip integral graded-polarized mixed period spaces with a natural ${\mathbb{R}}_{alg}$-definable analytic structure, and prove that any period map associated to an admissible variation of integral graded-polarized mixed Hodge structures is definable in ${\mathbb{R}}_{an,exp}$ with respect to this structure. As a consequence we reprove that the zero loci of admissible normal functions are algebraic.

15 pages. Comments welcome!