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

Shigefumi Mori; Yuri Prokhorov

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

Algebraic Geometry 2025-04-18 v2

Authors: Shigefumi Mori , Yuri Prokhorov

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~ $C$ .

Keywords

extremal contractions threefold one-dimensional fibers terminal singularities classification

Cite

@article{arxiv.2410.03165,
  title  = {Toward the classification of threefold extremal contractions with one-dimensional fibers},
  author = {Shigefumi Mori and Yuri Prokhorov},
  journal= {arXiv preprint arXiv:2410.03165},
  year   = {2025}
}

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32 page , LaTeX, revised version

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

Abstract

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