Invariant Theory In Cauchy Riemann Geometry And Applications To The Study Of Holomorphic Mappings
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Invariant Theory In Cauchy Riemann Geometry And Applications To The Study Of Holomorphic Mappings
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Author : Yuan Zhang
language : en
Publisher:
Release Date : 2009
Invariant Theory In Cauchy Riemann Geometry And Applications To The Study Of Holomorphic Mappings written by Yuan Zhang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Cauchy-Riemann equations categories.
In this dissertation, proper holomorphic maps between some types of CR manifolds have been studied. For non-degenerate holomorphic Segre maps between Hn and HN, the complexifications of Heisenberg hypersurfaces, we show that they possess a partial rigidity property when N [less than/equal to] 2n - 2. As an application under the same assumption, we prove that the holomorphic Segre non-transversality for these maps propagates along Segre varieties. this propagation property fails when N> 2n - 2. For any proper rational holomorphic map between complex balls, we derive a simple and explicit criterion when it is equivalent to a holomorphic polynomial map. This criterion is used to show that proper rational holomorphic maps from B2 into BN of degree two are equivalent to polynomial maps. For general smooth CR embeddings from a Levi non-degenerate hypersurface into another one with the same signature, a monotonicity property of the Chern-Moser-Weyl curvature along directions in the null space of the Levi-form has been obtained.
Geometric Invariant Theory
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Author : David Mumford
language : en
Publisher: Springer Science & Business Media
Release Date : 1994
Geometric Invariant Theory written by David Mumford and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
"Geometric Invariant Theory" by Mumford/Fogarty (the firstedition was published in 1965, a second, enlarged editonappeared in 1982) is the standard reference on applicationsof invariant theory to the construction of moduli spaces.This third, revised edition has been long awaited for by themathematical community. It is now appearing in a completelyupdated and enlarged version with an additional chapter onthe moment map by Prof. Frances Kirwan (Oxford) and a fullyupdated bibliography of work in this area.The book deals firstly with actions of algebraic groups onalgebraic varieties, separating orbits by invariants andconstructionquotient spaces; and secondly with applicationsof this theory to the construction of moduli spaces.It is a systematic exposition of the geometric aspects ofthe classical theory of polynomial invariants.
Geometric Invariant Theory Holomorphic Vector Bundles And The Harder Narasimhan Filtration
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Author : Alfonso Zamora Saiz
language : en
Publisher: Springer
Release Date : 2021-03-25
Geometric Invariant Theory Holomorphic Vector Bundles And The Harder Narasimhan Filtration written by Alfonso Zamora Saiz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-25 with Mathematics categories.
This book introduces key topics on Geometric Invariant Theory, a technique to obtaining quotients in algebraic geometry with a good set of properties, through various examples. It starts from the classical Hilbert classification of binary forms, advancing to the construction of the moduli space of semistable holomorphic vector bundles, and to Hitchin’s theory on Higgs bundles. The relationship between the notion of stability between algebraic, differential and symplectic geometry settings is also covered. Unstable objects in moduli problems -- a result of the construction of moduli spaces -- get specific attention in this work. The notion of the Harder-Narasimhan filtration as a tool to handle them, and its relationship with GIT quotients, provide instigating new calculations in several problems. Applications include a survey of research results on correspondences between Harder-Narasimhan filtrations with the GIT picture and stratifications of the moduli space of Higgs bundles. Graduate students and researchers who want to approach Geometric Invariant Theory in moduli constructions can greatly benefit from this reading, whose key prerequisites are general courses on algebraic geometry and differential geometry.
The Invariant Theory Of Matrices
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Author : Corrado De Concini
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-11-16
The Invariant Theory Of Matrices written by Corrado De Concini and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-16 with Invariants categories.
This book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation. Following Hermann Weyl's classical approach, the ring of invariants is described by formulating and proving (1) the first fundamental theorem that describes a set of generators in the ring of invariants, and (2) the second fundamental theorem that describes relations between these generators. The authors study both the case of matrices over a field of characteristic 0 and the case of matrices over a field of positive characteristic. While the case of characteristic 0 can be treated following a classical approach, the case of positive characteristic (developed by Donkin and Zubkov) is much harder. A presentation of this case requires the development of a collection of tools. These tools and their application to the study of invariants are exlained in an elementary, self-contained way in the book.
Stein Manifolds And Holomorphic Mappings
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Author : Franc Forstnerič
language : en
Publisher: Springer
Release Date : 2017-09-05
Stein Manifolds And Holomorphic Mappings written by Franc Forstnerič and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-05 with Mathematics categories.
This book, now in a carefully revised second edition, provides an up-to-date account of Oka theory, including the classical Oka-Grauert theory and the wide array of applications to the geometry of Stein manifolds. Oka theory is the field of complex analysis dealing with global problems on Stein manifolds which admit analytic solutions in the absence of topological obstructions. The exposition in the present volume focuses on the notion of an Oka manifold introduced by the author in 2009. It explores connections with elliptic complex geometry initiated by Gromov in 1989, with the Andersén-Lempert theory of holomorphic automorphisms of complex Euclidean spaces and of Stein manifolds with the density property, and with topological methods such as homotopy theory and the Seiberg-Witten theory. Researchers and graduate students interested in the homotopy principle in complex analysis will find this book particularly useful. It is currently the only work that offers a comprehensive introduction to both the Oka theory and the theory of holomorphic automorphisms of complex Euclidean spaces and of other complex manifolds with large automorphism groups.
Invariant Theory
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Author : Sebastian S. Koh
language : en
Publisher:
Release Date : 2014-01-15
Invariant Theory written by Sebastian S. Koh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Geometric Invariant Theory
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Author : David Mumford
language : en
Publisher: Springer
Release Date : 1994-04-12
Geometric Invariant Theory written by David Mumford and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-04-12 with Mathematics categories.
This standard reference on applications of invariant theory to the construction of moduli spaces is a systematic exposition of the geometric aspects of classical theory of polynomial invariants. This new, revised edition is completely updated and enlarged with an additional chapter on the moment map by Professor Frances Kirwan. It includes a fully updated bibliography of work in this area.
Lectures On Contact 3 Manifolds Holomorphic Curves And Intersection Theory
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Author : Chris Wendl
language : en
Publisher: Cambridge University Press
Release Date : 2020-03-26
Lectures On Contact 3 Manifolds Holomorphic Curves And Intersection Theory written by Chris Wendl and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-26 with Mathematics categories.
Intersection theory has played a prominent role in the study of closed symplectic 4-manifolds since Gromov's famous 1985 paper on pseudoholomorphic curves, leading to myriad beautiful rigidity results that are either inaccessible or not true in higher dimensions. Siefring's recent extension of the theory to punctured holomorphic curves allowed similarly important results for contact 3-manifolds and their symplectic fillings. Based on a series of lectures for graduate students in topology, this book begins with an overview of the closed case, and then proceeds to explain the essentials of Siefring's intersection theory and how to use it, and gives some sample applications in low-dimensional symplectic and contact topology. The appendices provide valuable information for researchers, including a concise reference guide on Siefring's theory and a self-contained proof of a weak version of the Micallef–White theorem.
Geometric Function Theory In Several Complex Variables
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Author : Carl H. FitzGerald
language : en
Publisher: World Scientific
Release Date : 2004
Geometric Function Theory In Several Complex Variables written by Carl H. FitzGerald and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
The papers contained in this book address problems in one and several complex variables. The main theme is the extension of geometric function theory methods and theorems to several complex variables. The papers present various results on the growth of mappings in various classes as well as observations about the boundary behavior of mappings, via developing and using some semi group methods.
Peterson S Annual Guides Graduate Study
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Author : Peterson's Guides, Inc
language : en
Publisher:
Release Date : 1982
Peterson S Annual Guides Graduate Study written by Peterson's Guides, Inc and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Education categories.