Cone Theorems and Cyclic Covers
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 C ⊂ X directly, we construct a covering Y → X and deform another morphism D → Y 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.
KeywordsIrreducible Component Complete Intersection Characteristic Zero Cartier Divisor Irreducible Curve
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