Ideal-adic semi-continuity of minimal log discrepancies on surfaces

TL;DR

This paper proves that minimal log discrepancies on algebraic surfaces exhibit ideal-adic semi-continuity, contributing to the understanding of singularity invariants in algebraic geometry.

Contribution

It establishes the ideal-adic semi-continuity property of minimal log discrepancies specifically for surfaces, a new result in the field.

Findings

Minimal log discrepancies are semi-continuous in the ideal-adic topology on surfaces.

The result advances the understanding of singularity measures in algebraic geometry.

Provides a foundation for further research on invariants in higher dimensions.

Abstract

We prove the ideal-adic semi-continuity of minimal log discrepancies on surfaces.