On the topology of a~complex-analytic normalization
Sbornik. Mathematics, Tome 40 (1981) no. 2, pp. 267-276
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In this paper the problem of constructing a normalization of a complex-analytic space is considered. The transition from a complex space to its normalization is carried out in two stages: in the first stage only the topology of the original space is changed; in the second stage “completion” of the structure sheaf takes place without change in the topology. The first stage is studied in detail; it is shown that an operation can be defined on the class of all pseudomanifolds which, applied to the body of the simplicial complex triangulating an irreducible complex space, gives a polyhedron homeomorphic to a normalization of the original space. It is also shown that this operation has the property of functoriality with respect to ramified coverings. A number of properties of such pseudomanifolds are obtained (in particular, it is shown that all of them are Cantor manifolds).
Bibliography: 9 titles.
@article{SM_1981_40_2_a9,
author = {I. V. Savel'ev},
title = {On the topology of a~complex-analytic normalization},
journal = {Sbornik. Mathematics},
pages = {267--276},
publisher = {mathdoc},
volume = {40},
number = {2},
year = {1981},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1981_40_2_a9/}
}
I. V. Savel'ev. On the topology of a~complex-analytic normalization. Sbornik. Mathematics, Tome 40 (1981) no. 2, pp. 267-276. http://geodesic.mathdoc.fr/item/SM_1981_40_2_a9/