Semi-continuity of Complex Singularity Exponents in Singular Central Fiber Cases

2012/11/07 by Yuchen Liu, Liu, Yuchen
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1211.1450

openalex publication_date 2012/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this new version, we add the proof of the main theorem when the central fiber is not necessarily simple normal crossing. We also correct some typos.

Citations

• IMPANGA lecture notes on log canonical thresholds
• Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I
• ACC for log canonical thresholds

Related

• Lelong numbers, complex singularity exponents, and Siu's semicontinuity theorem
• A note on singularity of fibers of singular sets
• A note on ξ-Bergman kernels
• Maximal contact and normal crossings in resolution of singularities
• Singularity invariants of plurisubharmonic functions and complex spaces