1996/05/23 by Marco Andreatta, Andreatta, Marco, Jarosław A. Wiśniewski +1 · 2 citations
Mathematics · #14E30 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #alg-geom #math.AG #msc:14E30
paper · pdf · doi:10.48550/arxiv.alg-geom/9605013
PlainTex, 58 pages
arxiv created 1996/05/23 · openalex publication_date 1996/05/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 -KX 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.