Algebraic Quotients. Torus Actions and Cohomology. The Adjoint Representation and the Adjoint Action
Algebraic Quotients. Torus Actions and Cohomology. The Adjoint Representation and the Adjoint Action

Author: A. Bialynicki-Birula

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 248

ISBN-13: 3662050714

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This is the second volume of the new subseries "Invariant Theory and Algebraic Transformation Groups". The aim of the survey by A. Bialynicki-Birula is to present the main trends and achievements of research in the theory of quotients by actions of algebraic groups. This theory contains geometric invariant theory with various applications to problems of moduli theory. The contribution by J. Carrell treats the subject of torus actions on algebraic varieties, giving a detailed exposition of many of the cohomological results one obtains from having a torus action with fixed points. Many examples, such as toric varieties and flag varieties, are discussed in detail. W.M. McGovern studies the actions of a semisimple Lie or algebraic group on its Lie algebra via the adjoint action and on itself via conjugation. His contribution focuses primarily on nilpotent orbits that have found the widest application to representation theory in the last thirty-five years.

Quotients
Quotients

Author: Tracy O'Neill

Publisher: Soho Press

Published: 2020-05-12

Total Pages: 392

ISBN-13: 1641291125

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Two people search for connection in a world of fractured identities and aliases, global finance, big data, intelligence bureaucracies, algorithmic logic, and terror. Jeremy Jordan and Alexandra Chen hope to make a quiet home together but struggle to find a space safe from their personal secrets. For Jeremy, this means leaving behind his former life as an intelligence operative during The Troubles in Northern Ireland. For Alexandra, a high-powered job in image management for whole countries cannot prepare her for her missing brother’s sudden reappearance. In a culture of limitless surveillance, Jeremy and Alexandra will go to great lengths to protect what is closest to them. Spanning decades and continents, their saga brings them into contact with a down-and-out online journalist, shadowy security professionals, and jockeying technology experts, each of whom has a different understanding of whether information really protects us, and how we might build a world worth trusting in our paranoid age.

Tree Form Quotients as Variables in Volume Estimation
Tree Form Quotients as Variables in Volume Estimation

Author: Gerald E. Hoyer

Publisher:

Published: 1985

Total Pages: 24

ISBN-13:

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De procedure van de Duitser Hohenadl voor het bepalen van vormquotienten (afgeleid van diverse stamdiameters) en de boominhoud (ook afgeleid van stamdiameters op vastgestelde hoogtes) wordt behandeld. De procedure in gewijzigde vormen werd toegepast op gegevens van de Tsuga hetrophylla. De beschreven procedure blijkt ook voor andere boomsoorten toepasbaar

The Geometry of some special Arithmetic Quotients
The Geometry of some special Arithmetic Quotients

Author: Bruce Hunt

Publisher: Springer

Published: 2006-11-14

Total Pages: 347

ISBN-13: 354069997X

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The book discusses a series of higher-dimensional moduli spaces, of abelian varieties, cubic and K3 surfaces, which have embeddings in projective spaces as very special algebraic varieties. Many of these were known classically, but in the last chapter a new such variety, a quintic fourfold, is introduced and studied. The text will be of interest to all involved in the study of moduli spaces with symmetries, and contains in addition a wealth of material which has been only accessible in very old sources, including a detailed presentation of the solution of the equation of 27th degree for the lines on a cubic surface.

Quantization of Singular Symplectic Quotients
Quantization of Singular Symplectic Quotients

Author: N.P. Landsman

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 360

ISBN-13: 3034883641

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This is the first exposition of the quantization theory of singular symplectic (Marsden-Weinstein) quotients and their applications to physics. The reader will acquire an introduction to the various techniques used in this area, as well as an overview of the latest research approaches. These involve classical differential and algebraic geometry, as well as operator algebras and noncommutative geometry. Thus one will be amply prepared to follow future developments in this field.

Compact Quotients of Cahen-Wallach Spaces
Compact Quotients of Cahen-Wallach Spaces

Author: Ines Kath

Publisher: American Mathematical Soc.

Published: 2020-02-13

Total Pages: 84

ISBN-13: 1470441039

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Indecomposable symmetric Lorentzian manifolds of non-constant curvature are called Cahen-Wallach spaces. Their isometry classes are described by continuous families of real parameters. The authors derive necessary and sufficient conditions for the existence of compact quotients of Cahen-Wallach spaces in terms of these parameters.

Quotients of Coxeter Complexes and $P$-Partitions
Quotients of Coxeter Complexes and $P$-Partitions

Author: Victor Reiner

Publisher: American Mathematical Soc.

Published: 1992

Total Pages: 146

ISBN-13: 0821825259

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This is a study of some of the combinatorial and topological properties of finite Coxeter complexes. The author begins by studying some of the general topological and algebraic properties of quotients of Coxeter complexes, and determines when they are pseudomanifolds (with or without boundary) and when they are Cohen-Macaulay or Gorenstein over a field. The paper also examines quotients of Coxeter complexes by cyclic subgroups generated by Coxeter elements.

Cohomology of Quotients in Symplectic and Algebraic Geometry. (MN-31), Volume 31
Cohomology of Quotients in Symplectic and Algebraic Geometry. (MN-31), Volume 31

Author: Frances Clare Kirwan

Publisher: Princeton University Press

Published: 2020-06-30

Total Pages: 216

ISBN-13: 0691214565

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These notes describe a general procedure for calculating the Betti numbers of the projective quotient varieties that geometric invariant theory associates to reductive group actions on nonsingular complex projective varieties. These quotient varieties are interesting in particular because of their relevance to moduli problems in algebraic geometry. The author describes two different approaches to the problem. One is purely algebraic, while the other uses the methods of symplectic geometry and Morse theory, and involves extending classical Morse theory to certain degenerate functions.

The Leadership Quotient
The Leadership Quotient

Author: Bill Service Ph.D.

Publisher: iUniverse

Published: 2006-03-23

Total Pages: 716

ISBN-13: 0595831230

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Now, there is a formula for leadership, the LQ. Like the Intelligence Quotient and the Emotional Quotient that preceded it, The Leadership Quotient contains verifiable dimensions of leadership that are designed to improve every leader's performance. The Leadership Quotient makes the complex simple by fitting the 12 dimensions of leadership into a framework of leader, follower, and environment. The Leadership Quotient makes the three components measurable and practical for the reader. The "nature vs. nurture" argument is over. There is general agreement that effective leaders are prepared by nature and refined by nurture. The need for improved leadership has never been greater, as witnessed by corporate scandals, world tumult, and economic morass. The failure of ethical moralities and the dumbing down of education give clarion calls for the type of improved leadership available through the application of LQ principles. The Leadership Quotient is thoroughly researched by two leadership experts, who combined, have 37 years of practical business leadership, 45 years of formal education, and 25 years of teaching leadership at the university level. Yet, the book is accessibly written for leadership practitioners. The LQ is years of comprehensive research packaged in a simplified formula for immediate application.

Analytic Quotients
Analytic Quotients

Author: Ilijas Farah

Publisher: American Mathematical Soc.

Published: 2000

Total Pages: 201

ISBN-13: 0821821172

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This book is intended for graduate students and research mathematicians interested in set theory.