Threefold extremal contractions of types (IC) and (IIB)

Details Threefold extremal contractions of types (IC) and (IIB) Threefold extremal contractions of types (IC) and (IIB)

2011-06-25

arxiv.org/abs/1106.5180v1

Mathematics

Algebraic Geometry

22 pages, LaTeX

Scientific paper

Let $(X,C)$ be a germ of a threefold $X$ with terminal singularities along an
irreducible reduced complete curve $C$ with a contraction $f: (X,C)\to (Z,o)$
such that $C=f^{-1}(o)_{red}$ and $-K_X$ is ample. Assume that $(X,C)$ contains
a point of type (IC) or (IIB). We complete the classification of such germs in
terms of a general member $H\in |\mathcal O_X|$ containing $C$.

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