Algebraic homogeneous spaces and invariant theory

by Frank D. Grosshans

Publisher: Springer in Berlin, New York

Written in English
Cover of: Algebraic homogeneous spaces and invariant theory | Frank D. Grosshans
Published: Pages: 148 Downloads: 277
Share This

Subjects:

  • Algebraic spaces,
  • Invariants,
  • Group actions (Mathematics)

Edition Notes

Includes bibliographical references (p. [138]-145) and index.

StatementFrank D. Grosshans.
SeriesLecture notes in mathematics,, 1673, Lecture notes in mathematics (Springer-Verlag) ;, 1673.
Classifications
LC ClassificationsQA3 .L28 no. 1673, QA244 .L28 no. 1673
The Physical Object
Paginationvi, 148 p. ;
Number of Pages148
ID Numbers
Open LibraryOL693900M
ISBN 103540636285
LC Control Number97041173

Invariant theory and superalgebras. Providence, R.I.: Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society. ISBN Grosshans, Frank D. (). Algebraic Homogeneous Spaces and Invariant Theory (Lecture Notes in Mathematics). Springer. ISBN Grosshans, G. D. (). Dustin Clausen (arithmetic geometry, algebraic K-theory) Elisenda Feliu (applied algebraic geometry, applications to mathematical biology) Lars H. Halle (d egenerations of K-trivial varieties, Néron models, Hilbert schemes, geometric invariant theory) Lars Hesselholt (arithmetic geometry, algebraic K-theory) Søren Galatius (moduli spaces). Some of the new results proved using these ideas are reviewed: multiplicative generalizations of the Horn and saturation conjectures, generalizations of Fulton's conjecture, the deformation of cohomology of homogeneous spaces, and the strange duality conjecture in the theory of vector bundles on algebraic . These notes develop the theory of algebraic curves from the viewpoint of modern algebraic geometry, but without excessive prerequisites. It assumed that the reader is familiar with some basic properties of rings, ideals, and polynomials. ( views) Homogeneous Spaces and Equivariant Embeddings by Dmitri A. Timashev - arXiv,

Algebraic Theory of Locally Nilpotent Derivations: Edition 2 - Ebook written by Gene Freudenburg. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Algebraic Theory . This project will focus on several topics regarding distribution of natural collections of points and orbits in Ln and more general arithmetic homogeneous spaces. We intend to use both spectral methods and dynamical methods to study these distribution problems, in combination with other tools such as invariant theory and combinatorics. Affinely closed, homogeneous spaces G/H, i.e., affine homogeneous spaces that admit only the trivial affine embedding, are characterized for an arbitrary affine algebraic group G. The representation theory of algebraic groups is developed using the framework of Hopf algebras, and actions of algebraic groups and homogeneous spaces are studied in detail. By the end of the eighth chapter, the reader has already been introduced to the basic concepts of (semi-)invariants and geometric quotients and may move on smoothly on to.

Book. Jan ; James E. Humphreys subseries "Invariant Theory and Algebraic Transformation Groups". The subject is homogeneous spaces of algebraic groups and their equivariant embeddings. Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view of their effect on functions. Classically, the theory dealt with the question of explicit description of polynomial functions that do not change, or a. Quotient spaces modulo reductive algebraic groups By C. S. SESHADRI Introduction In his book "Geometric invariant theory" [Ml, Mumford developed a theory of quotient spaces of algebraic schemes acted on by reductive algebraic groups when the ground field is of characteristic zero and showed how this can be used for several questions of moduli.

Algebraic homogeneous spaces and invariant theory by Frank D. Grosshans Download PDF EPUB FB2

The invariant theory of non-reductive groups has its roots in the 19th century but has seen some very interesting developments in the past twenty years.

This book is an exposition of several related topics including observable subgroups, induced modules, maximal unipotent subgroups of reductive groups and the method of U-invariants, and the. Algebraic Homogeneous Spaces and Invariant Theory Frank D. Grosshans (auth.) The invariant theory of non-reductive groups has its roots in the 19th century but has seen some very interesting developments in the past twenty years.

“This book is a survey of the study of equivariant embeddings of homogeneous spaces for connected reductive algebraic groups. The book is well written and puts together many results in a complete and concise manner.” (Lucy Moser-Jauslin, Mathematical Reviews, Issue e) “The book under review is concerned with the study of.

Algebraic homogeneous spaces and invariant theory. By Frank D Grosshans Cite. BibTex; Full citation The invariant theory of non-reductive groups has its roots in the 19th century but has seen some very interesting developments in the past twenty years. This book is an exposition of several related topics including observable subgroups Author: Frank D Grosshans.

The problems being solved by invariant theory are far-reaching generalizations and extensions of problems on the "reduction to canonical form" of various is almost the same thing, projective geometry.

objects of linear algebra or, what Invariant theory has a ISO-year history, which has seen alternating periods of growth and stagnation, and changes in the formulation of problems, methods of. It assumes only a minimal background in algebraic geometry, algebra and representation theory.

Topics covered include the symbolic method for computation of invariants on the space of homogeneous forms, the problem of finite-generatedness of the algebra of invariants, the theory of covariants and constructions of categorical and Algebraic homogeneous spaces and invariant theory book.

under the title "Lie Groups, Their Discrete Subgroups, and Invariant Theory" in The present volume is the second such collection. It consists mainly of original papers with new results in geometry and topology of homogeneous spaces of Lie groups, structure of Lie algebras, algebraic transformation groups, supermanifolds and Lie super.

Lie Groups and Invariant Theory About this Title. Ernest Vinberg, Moscow State University, Moscow, Russia, Editor. Publication: American Mathematical Society Translations: Series 2 Publication Year Volume ISBNs: (print); (online). 14) Wednesday: We finish studying the Classical invariant theory by covering the fundamental theorem for SL_n.

The we wrap up and start a new topic by discussing homogeneous spaces. References include [PV, Section 9], [OV, ]. 15) Monday: We talk more about homogeneous spaces and start to study U-invariants.

References include. Woodward on geometric invariant theory and its relation to symplectic reduction. Here is a brief overview of the contents. In the rst part, we begin with basic de nitions and properties of algebraic group actions, including the construction of homogeneous spaces under linear algebraic groups.

Get this from a library. Algebraic homogeneous spaces and invariant theory. [Frank D Grosshans]. Homogeneous spaces of linear algebraic groups lie at the crossroads of algebraic geometry, theory of algebraic groups, classical projective and enumerative geometry, harmonic analysis, and representation theory.

By standard reasons of algebraic geometry, in order to solve various problems on a homogeneous space, it is natural and helpful to.

‘This book is a detailed account of virtually every aspect of the general theory of the Cox ring of an algebraic variety. After a thorough introduction it takes the reader on an impressive tour through toric geometry, geometric invariant theory, Mori dream spaces, and universal torsors, culminating with applications to the Manin conjecture on.

Algebraic geometry From wikipedia: Algebraic geometryis a branch of mathematics, classically studying zeros of multivariate polynomials.

Han-Bom Moon Algebraic Geometry, Moduli Spaces, and Invariant Theory. This is a draft of a monograph to appear in the Springer series "Encyclopaedia of Mathematical Sciences", subseries "Invariant Theory and Algebraic Transformation Groups".

The subject is homogeneous spaces of algebraic groups and their equivariant embeddings. The style of exposition is intermediate between survey and detailed monograph: some results are supplied with. Get this from a library. Algebraic homogeneous spaces and invariant theory.

[Frank D Grosshans] -- The invariant theory of non-reductive groups has its roots in the 19th century but has seen some very interesting developments in the past twenty years. This book is an exposition of several related.

More than half a century has passed since Weyl's "The Classical Groups" gave a unified picture of invariant theory that has retained its importance in mathematics and physics to the present day. This book presents an updated version of this theory together with many of the important recent developments.

As a text for beginners, this book provides an introduction to the structure and finite. Thus the appearance of a book specifically devoted to projective duality is a long-awaited and welcome event. Projective Duality and Homogeneous Spaces covers a vast and diverse range of topics in the field of dual varieties, ranging from differential geometry to Mori theory and from topology to the theory of algebras.

It gives a very readable. This volume introduces the theory of prehomogeneous vector spaces, a field pioneered in the s by Mikio Sato. The author was an early and important developer of the theory and continues to be active in the field. The subject combines elements of several areas of mathematics, such as algebraic geometry, Lie groups, analysis, number theory, and invariant theory.

Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view of their effect on cally, the theory dealt with the question of explicit description of polynomial functions that do not change, or are invariant, under the transformations from a given linear group.

In recent years, there has been increasing interest and activity in the area of group actions on affine and projective algebraic varieties. Tech­ niques from various branches of mathematics have been important for this study, especially those coming from the well-developed theory of.

Lectures on Invariant Theory (London Mathematical Society Lecture Note Series Book ) - Kindle edition by Dolgachev, Igor.

Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Lectures on Invariant Theory (London Mathematical Society Lecture Note Series Book ).Reviews: 1.

Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view of their effect on cally, the theory dealt with the question of explicit description of polynomial functions that do not change, or are.

Introduction Linear algebraic groups and their homogeneous spaces have been thoroughly investigated; in par- cular, the Chow ring of a connected linear algebraic group G over an algebraically closed field k as determined by Grothendieck (see [Gr58, p. 21]), and the rational Chow ring of a G-homogeneous ace admits a simple description via Edidin.

Four Classes of Homogeneous Spaces. Two Problems. Remarks. Projective Characterization of the Basic Group. The Fundamental Theorems. The Grassmann Space. The Space of an Involutoric Correlation. The Invariant Elements.

The Space of a Null System. The Fundamental Theorem in the General Case. Applications. The Space of a Polar System and the. We study linear actions of algebraic groups on smooth projective varieties X. A guiding goal for us is to understand the cohomology of "quotients" under such actions, by generalizing (from reductive to non-reductive group actions) existing methods involving Mumford's geometric invariant theory (GIT).

We concentrate on actions of unipotent groups H, and define sets of stable points X^s and. Discover Algebraic Spaces by Donald Knutson and millions of other books available at Barnes & Noble.

Shop paperbacks, eBooks, and more. Our Stores Are Open Book Annex Membership Educators Gift Cards Stores & Events Help. This is a draft of a monograph to appear in the Springer series "Encyclopaedia of Mathematical Sciences", subseries "Invariant Theory and Algebraic Transformation Groups".

The subject is homogeneous spaces of algebraic groups and their equivariant embeddings. The style of exposition is intermediate between survey and detailed monograph: some results are supplied with detailed proofs.

Geometric invariant theory arises in an attempt to construct a quotient of an al-gebraic variety by an algebraic action of a linear algebraic group. In many applications is the parametrizing space of certain geometric objects (algebraic curves, vector bundles, etc.) and the equivalence relation on the objects is defined by a group action.

It assumes only a minimal background in algebraic geometry, algebra and representation theory. Topics covered include the symbolic method for computation of invariants on the space of homogeneous forms, the problem of finite-generatedness of the algebra of invariants, the theory of covariants and constructions of categorical and geometric.

Projective Duality and Homogeneous Spaces (Encyclopaedia of Mathematical Sciences Book ) - Kindle edition by Tevelev, Evgueni A.

Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Projective Duality and Homogeneous Spaces (Encyclopaedia of Mathematical Sciences Book ). Abstract: This is a draft of a monograph to appear in the Springer series "Encyclopaedia of Mathematical Sciences", subseries "Invariant Theory and Algebraic Transformation Groups".

The subject is homogeneous spaces of algebraic groups and their equivariant embeddings. The style of exposition is intermediate between survey and detailed monograph: some results are supplied with.

We associate to every divisorial (e.g., smooth) variety X with only constant invertible global functions and finitely generated Picard group a Pic(X)-graded homogeneous coordinate generalizes the usual homogeneous coordinate ring of the projective space and constructions of Cox and Kajiwara for smooth and divisorial toric varieties.