HOLOMORPHIC SELF-MAPS OF SINGULAR RATIONAL SURFACES

被引：18
作者：
Favre, Charles [1 ]
机构：
[1] Univ Paris 07, CNRS, Inst Math, F-75251 Paris 05, France
来源：
PUBLICACIONS MATEMATIQUES | 2010年 / 54卷 / 02期
关键词：
Rational maps; dynamics; surface singularity; valuation space; SMOOTH PROJECTIVE 3-FOLDS; KODAIRA DIMENSION; DEGREE GROWTH; ROOT SYSTEMS; ENDOMORPHISMS; DYNAMICS; AUTOMORPHISMS; VALUATIONS; MAPPINGS; GEOMETRY;
D O I：
10.5565/PUBLMAT_54210_06
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give a new proof of the classification of normal singular surface germs admitting non-invertible holomorphic self-maps and due to J. Wahl. We then draw an analogy between the birational classification of singular holomorphic foliations on surfaces, and the dynamics of holomorphic maps. Following this analogy, we introduce the notion of minimal holomorphic model for holomorphic maps. We give sufficient conditions which ensure the uniqueness of such a model.
引用
收藏
页码：389 / 432
页数：44
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