|
This article is cited in 1 scientific paper (total in 1 paper)
General elephants for threefold extremal contractions with one-dimensional fibres: exceptional case
S. Moriabc, Yu. G. Prokhorovd a Kyoto University Institute for Advanced Study, Kyoto University, Kyoto, Japan
b Research Institute for Mathematical Sciences, Kyoto University,
Kyoto, Japan
c Chubu University Academy of Emerging Sciences, Chubu University, Aichi, Japan
d Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
Abstract:
Let $(X, C)$ be a germ of a threefold $X$ with terminal singularities along a connected reduced complete curve $C$ with a contraction $f \colon (X, C) \to (Z, o)$ such that $C = f^{-1} (o)_{\mathrm{red}}$ and $-K_X$ is $f$-ample. Assume that each irreducible component of $C$ contains at most one point of index ${>2}$. We prove that a general member $D\in |{-}K_X|$ is a normal surface with Du Val singularities.
Bibliography: 16 titles.
Keywords:
terminal singularity, extremal curve germ, flip, divisorial contraction, $\mathbb{Q}$-conic bundle.
Received: 25.02.2020 and 27.11.2020
Citation:
S. Mori, Yu. G. Prokhorov, “General elephants for threefold extremal contractions with one-dimensional fibres: exceptional case”, Sb. Math., 212:3 (2021), 351–373
Linking options:
https://www.mathnet.ru/eng/sm9388https://doi.org/10.1070/SM9388 https://www.mathnet.ru/eng/sm/v212/i3/p88
|
Statistics & downloads: |
Abstract page: | 380 | Russian version PDF: | 39 | English version PDF: | 20 | Russian version HTML: | 130 | References: | 54 | First page: | 8 |
|