Viro theorem and topology of real and complex combinatorial hypersurfaces
Viro theorem and topology of real and complex combinatorial hypersurfaces
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DOI：
10.1007/bf02773068
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发表时间：
2003-01-01
影响因子：
1
通讯作者：
Shustin, E
中科院分区：
文献类型：
--
作者：
Itenberg, I;Shustin, E
在复射影空间中引入了一类组合超曲面。它们是CPN中余维为2的子流形，并且是(C*)(N)中代数超曲面的拓扑“粘合”出来的。我们的构造可以看作是Viro粘合定理的一个版本，它将代数超曲面的拓扑与凸格多面体的细分的组合联系起来。如果细分是凸的，则根据Viro定理，组合超曲面与代数超曲面是同质的。我们学习组合学。由凸多面体的非凸剖分生成的超曲面表明，它们几乎是复数簇，并且在实际情况下，它们满足相同的拓扑限制(同余、不等式等)。作为实代数超曲面。
We introduce a class of combinatorial hypersurfaces in the complex projective space. They are submanifolds of codimension 2 in CPn and are topologically "glued" out of algebraic hypersurfaces in (C*)(n). Our construction can be viewed as a version of the Viro gluing theorem, relating topology of algebraic hypersurfaces to the combinatorics of subdivisions of convex lattice polytopes. If a subdivision is convex, then according to the Viro theorem a combinatorial hypersurface is isotopic to an algebraic one. We study combinatorial. hypersurfaces resulting from non-convex subdivisions of convex polytopes, show that they are almost complex varieties, and in the real case, they satisfy the same topological restrictions (congruences, inequalities etc.) as real algebraic hypersurfaces.