Hypercomplex Varieties

Details Hypercomplex Varieties Hypercomplex Varieties

1997-03-12

arxiv.org/abs/alg-geom/9703016v1

Comm. Anal. Geom. 7 (1999), no. 2, 355--396.

Mathematics

Algebraic Geometry

40 pages LaTeX 2e

Scientific paper

We give a number of equivalent definitions of hypercomplex varieties and construct a twistor space for a hypercomplex variety. We prove that our definition of a hypercomplex variety (used, e. g., in alg-geom/9612013) is equivalent to a definition proposed by Deligne and Simpson, who used twistor spaces. This gives a way to define hypercomplex spaces (to allow nilpotents in the structure sheaf). We give a self-contained proof of desingularization theorem for hypercomplex varieties: a normalization of a hypercomplex variety is smooth and hypercomplex.

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