Numerical contraction for orbifold surfaces

TL;DR

This paper investigates singularities and contraction theorems for orbifold surfaces, contributing to the minimal model program by clarifying the nature of extremal contractions in b-terminal orbifold pairs.

Contribution

It provides new insights into the contraction behavior of orbifold surfaces, advancing the understanding of the minimal model program in this context.

Findings

Characterization of extremal contractions for b-terminal orbifold surfaces

Extension of Artin's contraction theorem to orbifold surfaces

Implications for the birational minimal model program

Abstract

We study singularities and Artin's contraction theorem for orbifold surfaces. Our main result has a consequence which is in the direction of the birational Minimal Model Program for b-terminal orbifold surfaces. For example, we ascertain the nature of extremal contractions for such $b$-terminal pairs.