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January, 2003 Models of rationally connected manifolds
Paltin IONESCU, Cristian VOICA
J. Math. Soc. Japan 55(1): 143-164 (January, 2003). DOI: 10.2969/jmsj/1196890847


We study rationally connected (projective) manifolds X via the concept of a model (X,Y), where Y is a smooth rational curve on X having ample normal bundle. Models are regarded from the view point of Zariski equivalence, birational on X and biregular around Y. Several numerical invariants of these objects are introduced and a notion of minimality is proposed for them. The important special case of models Zariski equivalent to (Pn,line) is investigated more thoroughly. When the (ample) normal bundle of Y in X has minimal degree, new such models are constructed via special vector bundles on X. Moreover, the formal geometry of the embedding of Y in X is analysed for some non-trivial examples.


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Paltin IONESCU. Cristian VOICA. "Models of rationally connected manifolds." J. Math. Soc. Japan 55 (1) 143 - 164, January, 2003.


Published: January, 2003
First available in Project Euclid: 5 December 2007

zbMATH: 1084.14052
MathSciNet: MR1939190
Digital Object Identifier: 10.2969/jmsj/1196890847

Primary: 14E25 , 14M99
Secondary: 14B20 , 14J45 , 14M20

Keywords: formal geometry , modej quasi-line , Rationally connected

Rights: Copyright © 2003 Mathematical Society of Japan


Vol.55 • No. 1 • January, 2003
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