Weak Semistable Reduction in Characteristic 0 Preliminary Version
نویسندگان
چکیده
0.1. The problem. Roughly speaking, the semistable reduction problem we address here asks for the following: Let X → B be a surjective morphism of complex projective varieties with geometrically integral generic fiber. Find a generically finite proper surjective morphism (that is, an alteration) B1 → B, and a proper birational morphism (that is, a modification) Y → X ×B B1, such that the morphism Y → B1 is nice. Of course, one needs to decide what a “nice morphism” means. The question was posed, among other places, in the introduction of [KKMS], p. vii. It can be viewed as a natural extension of Hironaka’s theorem on resolution of singularities, which is in a sense “the general fiber” of semistable reduction.
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