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Cone Theorems and Cyclic Covers

  • János Kollár

Abstract

This note is a continuation of [Kollár91b]. The aim is again to prove various forms of the Cone Theorem using methods similar to the original geometric arguments of [Mori79;82]. The basic idea is the same as in [Kollár91b]. Instead of deforming a curve CX directly, we construct a covering YX and deform another morphism DY whereD is a suitable covering of C. In [ibid], Y was a bug-eyed cover of X, therefore a nonseparated algebraic space. The method of this article is to replace X by its formal completion along C and then find a suitable cyclic covering Y of this formal scheme.

Keywords

Irreducible Component Complete Intersection Characteristic Zero Cartier Divisor Irreducible Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [Grothendieck62]
    A. Grothendieck, Fondements de la Geometric Algébrique, Sec. Math. Paris, 1962.Google Scholar
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    J. Kollar, Cone Theorems and Bug-eyed Covers, to appear.Google Scholar
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    A. Grothendieck, Revêtements Etales et Groupes Fondémentales, Springer LN 224, 1971.Google Scholar

Copyright information

© Springer-Verlag Tokyo 1991

Authors and Affiliations

  • János Kollár
    • 1
  1. 1.University of UtahSalt Lake CityUSA

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