THE KUGA–SATAKE CONSTRUCTION UNDER DEGENERATION

2017/10/31 by Stefan Schreieder, Andrey Soldatenkov · 4 citations
Mathematics · #Abelian group #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Degeneration (medical) #Geometry and complex manifolds #Hodge structure #Hodge theory #Limit (mathematics) #Type (biology) #math.AG

paper · pdf · doi:10.1017/s1474748019000239

published in Journal of the Institute of Mathematics of Jussieu 19(6), 2165-2182 (Cambridge University Press) · 16 pages; to appear in J. Inst. Math. Jussieu

openalex created_date 2017/10/20 · arxiv created 2019/03/29 · openalex publication_date 2019/05/17 · arxiv updated 2020/11/30 · openalex updated_date 2026/08/05

Abstract

We extend the Kuga–Satake construction to the case of limit mixed Hodge structures of K3 type. We use this to study the geometry and Hodge theory of degenerations of Kuga–Satake abelian varieties associated with polarized variations of K3 type Hodge structures over the punctured disc.

Citations

• Compactification of Arithmetic Quotients of Bounded Symmetric Domains
• Moduli of representations of the fundamental group of a smooth projective variety I