Ideal-adic semi-continuity problem for minimal log discrepancies
Masayuki Kawakita
TL;DR
This paper investigates the semi-continuity of minimal log discrepancies in algebraic geometry, proving semi-continuity in the case of Kawamata log terminal triples under ideal-adic deformations.
Contribution
It establishes the semi-continuity of minimal log discrepancies for Kawamata log terminal triples in the ideal-adic topology, advancing understanding in singularity theory.
Findings
Proves semi-continuity of minimal log discrepancies in the purely log terminal case.
Demonstrates deformation stability of minimal log discrepancies under ideal-adic topology.
Focuses on Kawamata log terminal triples in algebraic geometry.
Abstract
We discuss the ideal-adic semi-continuity problem for minimal log discrepancies by Mustata. We study the purely log terminal case, and prove the semi-continuity of minimal log discrepancies when a Kawamata log terminal triple deforms in the ideal-adic topology.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Analytic Number Theory Research · Cryptography and Residue Arithmetic