Patchworking real algebraic varieties
Patchworking real algebraic varieties
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拼凑实代数簇
DOI：
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发表时间：
2006
期刊：
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通讯作者：
O. Viro
中科院分区：
文献类型：
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作者：
O. Viro
拼接是构造一个单参数的真实的代数超曲面族。对于充分小的正值参数，超曲面可以通过给定的超曲面拓扑胶合得到。作者于1979- 1981年发明了拼接法，并将其用于构造具有复杂拓扑结构的真实的平面代数曲线。特别是，它有助于完成的非奇异平面投影真实的代数曲线的7度的合痕分类。拼接的一个特例，组合拼接，可以被认为是一个热带变种的李维诺夫-马斯洛夫量子化。由于其简单性，组合拼接比一般拼接更为人所知。本文是对拼缝的原创性介绍，充分体现了拼缝的一般性。
Patchworking is a construction of a one-parameter family of real algebraic hypersurfaces. For sufficiently small positive values of the parameter, the hypersurfaces can be obtained by gluing of given hypersurfaces topologically. The author invented patchworking in 1979-81 and used it for constructing of real plane algebraic curves with complicated prescribed topology. In particular, it helped to complete isotopy classification of nonsingular plane projective real algebraic curves of degree 7. A special case of the patchworking, combinatorial patchworking, can be considered as Litvinov-Maslov quantization of a tropical variety. Due to its simplicity, combinatorial patchworking is better known than the general one. This paper is the original presentation of the patchworking, in its full generality.