Flexibility Properties in Complex Analysis and Affine Algebraic Geometry

Kutzschebauch, Frank (2014). Flexibility Properties in Complex Analysis and Affine Algebraic Geometry. In: Cheltsov, Ivan; Ciliberto, Ciro; Flenner, Hubert; McKernan, James; Prokhorov, Yuri G.; Zaidenberg, Mikhail (eds.) Automorphisms in birational and affine geometry. Springer Proceedings in Mathematics & Statistics: Vol. 79 (pp. 387-405). Cham: Springer 10.1007/978-3-319-05681-4_22

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In the last decades affine algebraic varieties and Stein manifolds with big (infinite-dimensional) automorphism groups have been intensively studied. Several notions expressing that the automorphisms group is big have been proposed. All of them imply that the manifold in question is an Oka–Forstnerič manifold. This important notion has also recently merged from the intensive studies around the homotopy principle in Complex Analysis. This homotopy principle, which goes back to the 1930s, has had an enormous impact on the development of the area of Several Complex Variables and the number of its applications is constantly growing. In this overview chapter we present three classes of properties: (1) density property, (2) flexibility, and (3) Oka–Forstnerič. For each class we give the relevant definitions, its most significant features and explain the known implications between all these properties. Many difficult mathematical problems could be solved by applying the developed theory, we indicate some of the most spectacular ones.

Item Type:

Book Section (Book Chapter)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Kutzschebauch, Frank

Subjects:

500 Science > 510 Mathematics

ISBN:

978-3-319-05680-7

Series:

Springer Proceedings in Mathematics & Statistics

Publisher:

Springer

Language:

English

Submitter:

George Metcalfe

Date Deposited:

10 Aug 2015 08:37

Last Modified:

10 Aug 2015 08:39

Publisher DOI:

10.1007/978-3-319-05681-4_22

URI:

https://boris.unibe.ch/id/eprint/70815

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