Toward the classification of threefold extremal contractions with one-dimensional fibers

Shigefumi Mori; Yuri Prokhorov

paper

Toward the classification of threefold extremal contractions with one-dimensional fibers

arXiv:2410.03165

Abstract

An extremal curve germ is a germ of a threefold $X$ with terminal singularities along a connected reduced complete curve~ $C$ such that there exists a $K_{X}$ -negative contraction $f : X \to Z$ with~ $C$ being a fiber. We give a rough classification of extremal curve germs with reducible central curve~ $C$ .

arXiv comment32 page , LaTeX, revised version