Author: Javier Fernández de Bobadilla
Publisher: American Mathematical Soc.
ISBN: 0821835939
Category : Mathematics
Languages : en
Pages : 154
Book Description
Investigates the geometry of the orbit space. This book associates a graph with each polynomial in two variables that encodes part of its geometric properties at infinity. It also defines a partition of $\mathbb{C} x, y]$ imposing that the polynomials in the same stratum are the polynomials with a fixed associated graph
Moduli Spaces of Polynomials in Two Variables
Author: Javier Fernández de Bobadilla
Publisher: American Mathematical Soc.
ISBN: 0821835939
Category : Mathematics
Languages : en
Pages : 154
Book Description
Investigates the geometry of the orbit space. This book associates a graph with each polynomial in two variables that encodes part of its geometric properties at infinity. It also defines a partition of $\mathbb{C} x, y]$ imposing that the polynomials in the same stratum are the polynomials with a fixed associated graph
Publisher: American Mathematical Soc.
ISBN: 0821835939
Category : Mathematics
Languages : en
Pages : 154
Book Description
Investigates the geometry of the orbit space. This book associates a graph with each polynomial in two variables that encodes part of its geometric properties at infinity. It also defines a partition of $\mathbb{C} x, y]$ imposing that the polynomials in the same stratum are the polynomials with a fixed associated graph
Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $D$-Modules, Part 1
Author: Takuro Mochizuki
Publisher: American Mathematical Soc.
ISBN: 082183942X
Category : Mathematics
Languages : en
Pages : 344
Book Description
The author studies the asymptotic behaviour of tame harmonic bundles. First he proves a local freeness of the prolongment of deformed holomorphic bundle by an increasing order. Then he obtains the polarized mixed twistor structure from the data on the divisors. As one of the applications, he obtains the norm estimate of holomorphic or flat sections by weight filtrations of the monodromies. As another application, the author establishes the correspondence of semisimple regular holonomic $D$-modules and polarizable pure imaginary pure twistor $D$-modules through tame pure imaginary harmonic bundles, which is a conjecture of C. Sabbah. Then the regular holonomic version of M. Kashiwara's conjecture follows from the results of Sabbah and the author.
Publisher: American Mathematical Soc.
ISBN: 082183942X
Category : Mathematics
Languages : en
Pages : 344
Book Description
The author studies the asymptotic behaviour of tame harmonic bundles. First he proves a local freeness of the prolongment of deformed holomorphic bundle by an increasing order. Then he obtains the polarized mixed twistor structure from the data on the divisors. As one of the applications, he obtains the norm estimate of holomorphic or flat sections by weight filtrations of the monodromies. As another application, the author establishes the correspondence of semisimple regular holonomic $D$-modules and polarizable pure imaginary pure twistor $D$-modules through tame pure imaginary harmonic bundles, which is a conjecture of C. Sabbah. Then the regular holonomic version of M. Kashiwara's conjecture follows from the results of Sabbah and the author.
Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration
Author: Alfonso Zamora Saiz
Publisher: Springer Nature
ISBN: 3030678296
Category : Mathematics
Languages : en
Pages : 127
Book Description
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.
Publisher: Springer Nature
ISBN: 3030678296
Category : Mathematics
Languages : en
Pages : 127
Book Description
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 Complete Dimension Theory of Partially Ordered Systems with Equivalence and Orthogonality
Author: K. R. Goodearl
Publisher: American Mathematical Soc.
ISBN: 0821837168
Category : Mathematics
Languages : en
Pages : 134
Book Description
Introduction Partial commutative monoids Continuous dimension scales Espaliers Classes of espaliers Bibliography Index
Publisher: American Mathematical Soc.
ISBN: 0821837168
Category : Mathematics
Languages : en
Pages : 134
Book Description
Introduction Partial commutative monoids Continuous dimension scales Espaliers Classes of espaliers Bibliography Index
Representation Type of Commutative Noetherian Rings III: Global Wildness and Tameness
Author: Lee Klingler
Publisher: American Mathematical Soc.
ISBN: 0821837389
Category : Mathematics
Languages : en
Pages : 187
Book Description
This memoir completes the series of papers beginning with [KL1,KL2], showing that, for a commutative noetherian ring $\Lambda$, either the category of $\Lambda$-modules of finite length has wild representation type or else we can describe the category of finitely generated $\Lambda$-modules, including their direct-sum relations and local-global relations. (There is a possible exception to our results, involving characteristic 2.)
Publisher: American Mathematical Soc.
ISBN: 0821837389
Category : Mathematics
Languages : en
Pages : 187
Book Description
This memoir completes the series of papers beginning with [KL1,KL2], showing that, for a commutative noetherian ring $\Lambda$, either the category of $\Lambda$-modules of finite length has wild representation type or else we can describe the category of finitely generated $\Lambda$-modules, including their direct-sum relations and local-global relations. (There is a possible exception to our results, involving characteristic 2.)
Entropy Bounds and Isoperimetry
Author: Serguei Germanovich Bobkov
Publisher: American Mathematical Soc.
ISBN: 082183858X
Category : Computers
Languages : en
Pages : 88
Book Description
In these memoirs Bobkov and Zegarlinski describe interesting developments in infinite dimensional analysis that moved it away from experimental science. Here they also describe Poincar -type inequalities, entropy and Orlicz spaces, LSq and Hardy-type inequalities on the line, probability measures satisfying LSq inequalities on the real line, expo
Publisher: American Mathematical Soc.
ISBN: 082183858X
Category : Computers
Languages : en
Pages : 88
Book Description
In these memoirs Bobkov and Zegarlinski describe interesting developments in infinite dimensional analysis that moved it away from experimental science. Here they also describe Poincar -type inequalities, entropy and Orlicz spaces, LSq and Hardy-type inequalities on the line, probability measures satisfying LSq inequalities on the real line, expo
Flat Level Set Regularity of $p$-Laplace Phase Transitions
Author: Enrico Valdinoci
Publisher: American Mathematical Soc.
ISBN: 0821839101
Category : Mathematics
Languages : en
Pages : 158
Book Description
We prove a Harnack inequality for level sets of $p$-Laplace phase transition minimizers. In particular, if a level set is included in a flat cylinder, then, in the interior, it is included in a flatter one. The extension of a result conjectured by De Giorgi and recently proven by the third author for $p=2$ follows.
Publisher: American Mathematical Soc.
ISBN: 0821839101
Category : Mathematics
Languages : en
Pages : 158
Book Description
We prove a Harnack inequality for level sets of $p$-Laplace phase transition minimizers. In particular, if a level set is included in a flat cylinder, then, in the interior, it is included in a flatter one. The extension of a result conjectured by De Giorgi and recently proven by the third author for $p=2$ follows.
A Generating Function Approach to the Enumeration of Matrices in Classical Groups over Finite Fields
Author: Jason Fulman
Publisher: American Mathematical Soc.
ISBN: 0821837060
Category : Mathematics
Languages : en
Pages : 104
Book Description
Generating function techniques are used to study the probability that an element of a classical group defined over a finite field is separable, cyclic, semisimple or regular. The limits of these probabilities as the dimension tends to infinity are calculated in all cases, and exponential convergence to the limit is proved. These results complement and extend earlier results of the authors, G. E. Wall, and Guralnick & Lubeck.
Publisher: American Mathematical Soc.
ISBN: 0821837060
Category : Mathematics
Languages : en
Pages : 104
Book Description
Generating function techniques are used to study the probability that an element of a classical group defined over a finite field is separable, cyclic, semisimple or regular. The limits of these probabilities as the dimension tends to infinity are calculated in all cases, and exponential convergence to the limit is proved. These results complement and extend earlier results of the authors, G. E. Wall, and Guralnick & Lubeck.
The Second Duals of Beurling Algebras
Author: Harold G. Dales
Publisher: American Mathematical Soc.
ISBN: 0821837745
Category : Mathematics
Languages : en
Pages : 206
Book Description
Let $A$ be a Banach algebra, with second dual space $A""$. We propose to study the space $A""$ as a Banach algebra. There are two Banach algebra products on $A""$, denoted by $\,\Box\,$ and $\,\Diamond\,$. The Banach algebra $A$ is Arens regular if the two products $\Box$ and $\Diamond$ coincide on $A""$.
Publisher: American Mathematical Soc.
ISBN: 0821837745
Category : Mathematics
Languages : en
Pages : 206
Book Description
Let $A$ be a Banach algebra, with second dual space $A""$. We propose to study the space $A""$ as a Banach algebra. There are two Banach algebra products on $A""$, denoted by $\,\Box\,$ and $\,\Diamond\,$. The Banach algebra $A$ is Arens regular if the two products $\Box$ and $\Diamond$ coincide on $A""$.
Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations
Author: Greg Hjorth
Publisher: American Mathematical Soc.
ISBN: 0821837710
Category : Mathematics
Languages : en
Pages : 126
Book Description
Contributes to the theory of Borel equivalence relations, considered up to Borel reducibility, and measures preserving group actions considered up to orbit equivalence. This title catalogs the actions of products of the free group and obtains additional rigidity theorems and relative ergodicity results in this context.
Publisher: American Mathematical Soc.
ISBN: 0821837710
Category : Mathematics
Languages : en
Pages : 126
Book Description
Contributes to the theory of Borel equivalence relations, considered up to Borel reducibility, and measures preserving group actions considered up to orbit equivalence. This title catalogs the actions of products of the free group and obtains additional rigidity theorems and relative ergodicity results in this context.