
The Lefschetz Properties
Springer (Publisher)
1st Edition
Published on 30. August 2013
Book
Paperback/Softback
XIX, 250 pages
978-3-642-38205-5 (ISBN)
Description
This is a monograph which collects basic techniques, major results and interesting applications of Lefschetz properties of Artinian algebras. The origin of the Lefschetz properties of Artinian algebras is the Hard Lefschetz Theorem, which is a major result in algebraic geometry. However, for the last two decades, numerous applications of the Lefschetz properties to other areas of mathematics have been found, as a result of which the theory of the Lefschetz properties is now of great interest in its own right. It also has ties to other areas, including combinatorics, algebraic geometry, algebraic topology, commutative algebra and representation theory. The connections between the Lefschetz property and other areas of mathematics are not only diverse, but sometimes quite surprising, e.g. its ties to the Schur-Weyl duality. This is the first book solely devoted to the Lefschetz properties and is the first attempt to treat those properties systematically.
More details
Product info
Paperback
Series
Edition
2013
Language
English
Place of publication
Heidelberg
Germany
Publishing group
Springer Berlin
Target group
College/higher education
Research
Illustrations
6
20 s/w Abbildungen, 6 s/w Tabellen
XIX, 250 p. 20 illus.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 15 mm
Weight
417 gr
ISBN-13
978-3-642-38205-5 (9783642382055)
DOI
10.1007/978-3-642-38206-2
Schweitzer Classification
Other editions
Additional editions

Tadahito Harima | Toshiaki Maeno | Hideaki Morita
The Lefschetz Properties
E-Book
08/2013
Springer
€58.84
Available for download
Content
Introduction and Historical Note.- 1. Poset Theory.- 2. Basics on the Theory of Local Rings.- 3. Lefschetz Properties.- 4. Compete Intersections with the SLP.- 5. A Generalization of Lefschetz Elements.- 6. k-Lefschetz Properties.- 7. Cohomology Rings.- 8. Invariant Theory and Lefschetz Property.- 9. The Strong Lefschetz Property and the Schur-Weyl Duality.