2016/10/31 by Hülya Argüz
Mathematics · #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #Geometry and complex manifolds #Lift (data mining) #Point (geometry) #Space (punctuation) #Topology (electrical circuits) #Toric variety #Tropical geometry #math.AG #msc:14J32 #msc:14J33 #msc:14P05
paper · pdf · doi:10.1007/s40879-021-00454-z
published as European Journal of Mathematics, 2021 · 67 pages, 6 figures. Minor corrections thanks to an anonymous referee. Final version
openalex created_date 2020/05/13 · arxiv created 2021/01/20 · openalex publication_date 2021/03/23 · arxiv updated 2021/07/20 · openalex updated_date 2026/08/05
We study the real loci of toric degenerations of complex varieties with reducible central fibre. We show that the topology of such degenerations can be explicitly described via the Kato-Nakayama space of the central fibre as a log space. We furthermore provide generalities of real structures in log geometry and their lift to Kato-Nakayama spaces. A key point of this paper is a description of the Kato-Nakayama space of a toric degeneration and its real locus, both as bundles determined by combinatorial data. We provide several examples including real toric degenerations of K3-surfaces and a toric degeneration of local \textbbP2.