Definability of mixed period maps

Benjamin Bakker , Yohan Brunebarbe (1, 2) , Bruno Klingler (3) , Jacob Tsimerman

1 CNRS - Centre National de la Recherche Scientifique
2 IMB - Institut de Mathématiques de Bordeaux
3 HU Berlin - Humboldt-Universität zu Berlin = Humboldt University of Berlin = Université Humboldt de Berlin

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.

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]; Logique [math.LO]

Benjamin Bakker, Yohan Brunebarbe, Bruno Klingler, Jacob Tsimerman. Definability of mixed period maps. 2020. ⟨hal-03064630⟩