Extensions of Holomorphic Functions in Toric Varieties
The Hartogs and the Hartogs-Bochner Extension Phenomena obtained with the use of the Ends and the Cohomology Groups with Compact Supports
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This monograph treats classical complex analysisproblems considered for toric varieties. Theseproblems were originally posed and solved on complexn-spaces; and they are very difficult if consideredfor an arbitrary complex manifold.The author describes the Hartogs and theHartogs-Bochner extension phenomena in smooth toricvarieties and their connection with the firstcohomology group with compact supports. The mainproblem with compact sets, which appear in theHartogs phenomena, is that a compact set cut into aparticular coordinate patch does not have to remaincompact. Therefore, a global view of ...
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.
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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