The geometric minimal models of analytic spaces

Details The geometric minimal models of analytic spaces The geometric minimal models of analytic spaces

2001-12-13

arxiv.org/abs/math/0112134v1

Mathematics

Algebraic Geometry

16 pages

Scientific paper

This paper shows that an analytic space $X$ has a unique maximal model through which every proper surjective morphism from a non-singular analytic space to $X$ factors. This is called the {\sl geometric minimal model} of $X$ and characterized by the contraction property of rational curves. Some other properties such as functoriality, the direct product property and the quotient property of the geometric minimal model are also studied here. The relation of the geometric minimal model with Mori's minimal model is discussed.

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