Local models of Shimura varieties, I. Geometry and combinatorics

Details Local models of Shimura varieties, I. Geometry and combinatorics Local models of Shimura varieties, I. Geometry and combinatorics

2010-11-25

arxiv.org/abs/1011.5551v3

Mathematics

Algebraic Geometry

86 pages, small corrections and improvements, to appear in the "Handbook of Moduli"

Scientific paper

We survey the theory of local models of Shimura varieties. In particular, we discuss their definition and illustrate it by examples. We give an overview of the results on their geometry and combinatorics obtained in the last 15 years. We also exhibit their connections to other classes of algebraic varieties such as nilpotent orbit closures, affine Schubert varieties, quiver Grassmannians and wonderful completions of symmetric spaces.

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