Extremal contractions from 4-dimensional manifolds to 3-folds

Yasuyuki Kachi

Extremal contractions from 4-dimensional manifolds to 3-folds

alg-geom 2008-02-03 v1 Algebraic Geometry

Authors: Yasuyuki Kachi

Abstract

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 $g\text{-free}$ .

Keywords

extremal contractions 4-folds 3-folds rational curves fiber classification canonical divisor

Cite

@article{arxiv.alg-geom/9502023,
  title  = {Extremal contractions from 4-dimensional manifolds to 3-folds},
  author = {Yasuyuki Kachi},
  journal= {arXiv preprint arXiv:alg-geom/9502023},
  year   = {2008}
}

Comments

65 pages, TeX dialect: amsppt

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