On Contractions of smooth varieties

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Let $\f: X \ra Z$ be a proper surjective map from a smooth complex manifold $X$ onto a normal variety $Z$. If $\f$ has connected fibers and $-K_X$ is $\f$-ample then $\f$ is called a good contraction. In the present paper we study good contractions, fibers of which have dimension less or equal than two: after describing possible two dimensional isolated fibers we discuss their scheme theoretic structure and the geometry of $\f:X\ra Z$ nearby such a fiber. If $dimX=4$ and $\f$ is birational with an isolated 2 dimensional fiber then we obtain a complete description of $\f$. We provide also a description of a 4 dimensional conic fibration with an isolated fiber which is either a plane or a quadric. We construct pertinent examples.
PlainTex, 58 pages

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Algebraic Geometry, 14E30

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http://salesiana.dossiersoluciones.com/handle/123456789/150151

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/alg-geom/9605013
 http://arxiv.org/abs/alg-geom/9605013

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arXiv