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 - Softcover

Marciniak, Malgorzata

Softcover

ISBN 10: 3639169484 ISBN 13: 9783639169485

Publisher: VDM Verlag, 2009

Synopsis

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.

About this title

About the Author

Ma¿gorzata Aneta Marciniak, Ph.D., studied Mathematics at the University of Warsaw and at the Missouri University of Science and Technology. She has given multiple presentations for mathematical societies including research talks during special sessions of AMS meetings. She has been a member of AMS and MAA since January 2006.

Edition details

• Publisher: VDM Verlag
• Publication date: 2009
• Language: English
• ISBN 10: 3639169484
• ISBN 13: 9783639169485
• Binding: Paperback
• Number of pages: 124