Divisorial extractions from singular curves in a smooth 3-fold, II: low codimension

TL;DR

This paper extends the study of Mori extractions from singular curves in smooth 3-folds, focusing on cases where the extraction occurs in relative codimension up to 3, thereby broadening understanding of these geometric transformations.

Contribution

It provides a detailed analysis of divisorial extractions in low codimension cases, advancing the classification of such transformations in algebraic geometry.

Findings

Classification of divisorial extractions in codimension ≤ 3

Identification of conditions for existence of Mori extractions

Extension of previous results to broader cases

Abstract

Following the first paper, we continue to study Mori extractions from singular curves centred in a smooth 3-fold. We treat the case where the divisorial extraction exists in relative codimension at most 3.