Classification of Toric Surface Singularities

F. Ambro

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, P.O. BOX 1-764, RO-014700 Bucharest, Romania

Abstract: We classify two-dimensional toric log germs in terms of their minimal log discrepancy. In particular, Borisov's series of toric surface singularities with minimal log discrepancy bounded below can be described explicitly and geometrically.

Keywords: toric singularities, minimal log discrepancies, hyperplane sections.

Received: September 27, 2024
Revised: January 3, 2025
Accepted: January 23, 2025

DOI: 10.4213/tm4456

 English version: Proceedings of the Steklov Institute of Mathematics, 2025, 329, 1–13

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