Real loci in (log) Calabi–Yau manifolds via Kato–Nakayama spaces of toric degenerations

Journal article

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 tropical data. We provide several examples including real toric degenerations of K3-surfaces and a toric degeneration of local 

Authors: Argüz, H

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: European Journal of Mathematics
• Volume: 7
• Issue: 3
• Pages: 869-930
• Publication date: 2021-03-23
• Acceptance date: 2021-01-19
• DOI: 10.1007/s40879-021-00454-z
• EISSN: 2199-6768
• ISSN: 2199-675X
• Language: English
• Keywords: real log geometry; Kato–Nakayama spaces; degenerations; torus fibrations