Cone Theorems and Cyclic Covers

  • János Kollár


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.


Irreducible Component Complete Intersection Characteristic Zero Cartier Divisor Irreducible Curve 
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Copyright information

© Springer-Verlag Tokyo 1991

Authors and Affiliations

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

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