The Moment-Weight Inequality and the Hilbe...

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Beschreibung

This book provides an introduction to geometric invariant theory from a differential geometric viewpoint. It is inspired by certain infinite-dimensional analogues of geometric invariant theory that arise naturally in several different areas of geometry. The central ingredients are the moment-weight inequality relating the Mumford numerical invariants to the norm of the moment map, the negative gradient flow of the moment map squared, and the Kempf--Ness function. The exposition is essentially self-contained, except for an appeal to the Lojasiewicz gradient inequality. A broad variety of examples illustrate the theory, and five appendices cover essential topics that go beyond the basic concepts of differential geometry. The comprehensive bibliography will be a valuable resource for researchers.

The book is addressed to graduate students and researchers interested in geometric invariant theory and related subjects. It will be easily accessible to readers with a basic understanding of differential geometry and does not require any knowledge of algebraic geometry.

Über den Autor

Valentina Georgoulas was born in Zürich in 1978. She studied theoretical physics at ETH Zürich, where she received her master degree in 2008. She then went on to doctoral studies in mathematics and in 2016 completed her PhD in mathematics at ETH Zürich under the direction of Dietmar Salamon. After further training, she now works as a high school teacher for mathematics at MNG Rämibühl in Zürich. She is the mother of two children.

Joel W. Robbin was born in Chicago in 1941 and completed his PhD at Princeton University in 1965 under the direction of Alonzo Church. After a postdoctoral position in Princeton he took up an Assistant Professorship at the University of Wisconsin-Madson in 1967, where he became full Professor in 1973, and emeritus in 2010. Joel Robbin began his research in mathematical logic (and wrote a text book on this subject) and later moved on to dynamical systems and symplectic topology. In 1970 he proved a conjecture by Stephen Smale which asserts that Axiom A implies structural stability. His publications include a book on "Matrix Algebra" and a joint book with Ralph Abraham on "Transversal Mappings and Flows". He is a Fellow of the American Mathematical Society.

Dietmar A. Salamon was born in Bremen in 1953 and completed his PhD at the University of Bremen in 1982 under the direction of Diederich Hinrichsen. After postdoctoral positions in Madison and Zrich, he took up a position at the University Warwick in 1986, and moved to ETH Zurich in 1998. His field of research is symplectic topology and related subjects. He was an invited speaker at the ECM 1992 in Paris, at the ICM 1994 in Zurich, and at the ECM 2000 in Barcelona. He delivered the Andrejewski Lectures in Goettingen (1998) and at the Humboldt Unversity Berlin (2005), and the Xth Lisbon Summer lectures in Geometry (2009). He is the author of several text books and research momgraphs including two joint books with Dusa McDuff entitled "Introduction to Symplectic Topology" and "J-holomorphic Curves and Symplectic Topology" for which they received the Leroy P. Steele Prize for Mathematical Exposition in 2017.

Zusammenfassung

Provides the first complete and thorough treatment of GIT from a differential geometric viewpoint

Treats Hamiltonian group actions on general, not necessarily projective, compact Kähler manifolds

Presents another route to many of the main results of Mumford's theory which will have long lasting significance

Inhaltsverzeichnis

- Introduction. - The Moment Map. - The Moment Map Squared. - The Kempf-Ness Function. - ¿-Weights. - The Moment-Weight Inequality. - Stability in Symplectic Geometry. - Stability in Algebraic Geometry. - Rationality. - The Dominant ¿-Weight. - Torus Actions. - The Hilbert-Mumford Criterion. - Critical Orbits.

Erscheinungsjahr:	2021
Fachbereich:	Geometrie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	vii 192 S. 3 farbige Illustr. 192 p. 3 illus. in color.
ISBN-13:	9783030892999
ISBN-10:	3030892999
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Georgoulas, Valentina Salamon, Dietmar Arno Robbin, Joel W.
Auflage:	1st edition 2021
Hersteller:	Springer Nature Switzerland Springer International Publishing
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 12 mm
Von/Mit:	Valentina Georgoulas (u. a.)
Erscheinungsdatum:	21.11.2021
Gewicht:	0,312 kg

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