Geodesic
General elephants for threefold extremal contractions with one-dimensional fibres: exceptional case
Sbornik. Mathematics, Tome 212 (2021) no. 3, pp. 351-373

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{SM_2021_212_3_a6,
     author = {S. Mori and Yu. G. Prokhorov},
     title = {General elephants for threefold extremal contractions with one-dimensional fibres: exceptional case},
     journal = {Sbornik. Mathematics},
     pages = {351--373},
     publisher = {mathdoc},
     volume = {212},
     number = {3},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2021_212_3_a6/}
}
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S. Mori; Yu. G. Prokhorov. General elephants for threefold extremal contractions with one-dimensional fibres: exceptional case. Sbornik. Mathematics, Tome 212 (2021) no. 3, pp. 351-373. http://geodesic.mathdoc.fr/item/SM_2021_212_3_a6/