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Luna's Slice Theorem and applications.

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Titel: Luna's Slice Theorem and applications.
Autoren: Brion, Michel1 (AUTHOR), Kraft, Hanspeter2 (AUTHOR), Schwarz, Gerald W.3 (AUTHOR)
Quelle: Bulletin (New Series) of the American Mathematical Society. Oct2025, Vol. 62 Issue 4, p643-694. 52p.
Schlagwörter: *TRANSFORMATION groups, *ALGEBRAIC geometry, *ORBIT method, *LINEAR algebraic groups, *LAYPERSONS, *MATHEMATICS theorems
Abstract: The aim of this article is to give an introduction to Luna's Slice Theorem for nonspecialists. In the first section we give an idea of its significance without being too precise. It is followed by an introduction to compact transformation groups in Section 2. Then we show by examples how classification problems lead to the study of orbits of algebraic groups in Section 3. In order to explain and formulate Luna's Slice Theorem, we need some basics from algebraic transformation groups and algebraic geometry; this is done in Sections 4 and 5. The paper ends with some striking applications in Section 6. [ABSTRACT FROM AUTHOR]
Datenbank: Academic Search Index
Beschreibung
Abstract:The aim of this article is to give an introduction to Luna's Slice Theorem for nonspecialists. In the first section we give an idea of its significance without being too precise. It is followed by an introduction to compact transformation groups in Section 2. Then we show by examples how classification problems lead to the study of orbits of algebraic groups in Section 3. In order to explain and formulate Luna's Slice Theorem, we need some basics from algebraic transformation groups and algebraic geometry; this is done in Sections 4 and 5. The paper ends with some striking applications in Section 6. [ABSTRACT FROM AUTHOR]
ISSN:02730979
DOI:10.1090/bull/1872