Extremal contractions from 4-dimensional manifolds to 3-folds

Details Extremal contractions from 4-dimensional manifolds to 3-folds Extremal contractions from 4-dimensional manifolds to 3-folds

1995-02-25

arxiv.org/abs/alg-geom/9502023v1

Mathematics

Algebraic Geometry

65 pages, TeX dialect: amsppt

Scientific paper

Let $g : X \to Y$ be the contraction of an extremal ray of a smooth projective 4-fold $X$ such that $\dim Y=3$. Then $g$ may have a finite number of 2-dimensional fibers. We shall classify those fibers. Especially we shall prove that any two points of such a fiber is joined by a chain of rational curves of length at most 2 with respect to $-K_X$, and that $|-K_X|$ is $g\text{-free}$.

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