Threefold extremal contractions of type (IIA), II

TL;DR

This paper investigates threefold extremal contractions of type (IIA) with terminal singularities along a curve, extending previous work to classify and understand their structure and properties.

Contribution

It provides a detailed analysis of threefold extremal contractions of type (IIA), expanding the classification of such singularities and their geometric configurations.

Findings

Classification of extremal contractions of type (IIA)

Identification of singularity structures along the curve

Extension of previous classification results

Abstract

Let $(X, C)$ be a germ of a threefold $X$ with terminal singularities along an irreducible reduced complete curve $C$ with a contraction $f: (X, C)\to (Z, o)$ such that $C=f^{-1}(o)_{red}$ and $-K_X$ is ample. Assume that $(X, C)$ contains a point of type (IIA). This paper continues our study of such germs containing a point of type (IIA) started in our previous paper arXiv:1601.07671.