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Extensions of Holomorphic Functions in Toric Varieties
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Carte broșată
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Carte broșată
214
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This monograph treats classical complex analysis§problems considered for toric varieties. These§problems were originally posed and solved on complex§n-spaces; and they are very difficult if considered§for an arbitrary complex manifold.§The author describes the Hartogs and the§Hartogs-Bochner extension phenomena in smooth toric§varieties and their connection with the first§cohomology group with compact supports. The main§problem with compact sets, which appear in the§Hartogs phenomena, is that a compact set cut into a§particular coordinate patch does not have to remain§compact. Therefore, a global view of compact sets is§absolutely necessary for this problem. The§affirmative and negative results are proved using§topological, analytic, and algebraic methods. The§monograph is suitable for junior and senior§mathematicians interested in the theory of several§complex variables, toric varieties, and ends of§topological spaces.
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