Points on Quantum Projectivizations
Author:
Publisher: American Mathematical Soc.
Published:
Total Pages: 154
ISBN-13: 0821834959
DOWNLOAD EBOOK →Author:
Publisher: American Mathematical Soc.
Published:
Total Pages: 154
ISBN-13: 0821834959
DOWNLOAD EBOOK →Author: Adam Nyman
Publisher: American Mathematical Soc.
Published: 2003-12-17
Total Pages: 162
ISBN-13: 9780821865170
DOWNLOAD EBOOK →The use of geometric invariants has recently played an important role in the solution of classification problems in non-commutative ring theory. We construct geometric invariants of non-commutative projectivizataions, a significant class of examples in non-commutative algebraic geometry. More precisely, if $S$ is an affine, noetherian scheme, $X$ is a separated, noetherian $S$-scheme, $\mathcal{E}$ is a coherent ${\mathcal{O}}_{X}$-bimodule and $\mathcal{I} \subset T(\mathcal{E})$ is a graded ideal then we develop a compatibility theory on adjoint squares in order to construct the functor $\Gamma_{n}$ of flat families of truncated $T(\mathcal{E})/\mathcal{I}$-point modules of length $n+1$. For $n \geq 1$ we represent $\Gamma_{n}$ as a closed subscheme of ${\mathbb{P}}_{X^{2}}({\mathcal{E}}^{\otimes n})$. The representing scheme is defined in terms of both ${\mathcal{I}}_{n}$ and the bimodule Segre embedding, which we construct. Truncating a truncated family of point modules of length $i+1$ by taking its first $i$ components defines a morphism $\Gamma_{i} \rightarrow \Gamma_{i-1}$ which makes the set $\{\Gamma_{n}\}$ an inverse system. In order for the point modules of $T(\mathcal{E})/\mathcal{I}$ to be parameterizable by a scheme, this system must be eventually constant. In [20], we give sufficient conditions for this system to be constant and show that these conditions are satisfied when ${\mathsf{Proj}} T(\mathcal{E})/\mathcal{I}$ is a quantum ruled surface. In this case, we show the point modules over $T(\mathcal{E})/\mathcal{I}$ are parameterized by the closed points of ${\mathbb{P}}_{X^{2}}(\mathcal{E})$.
Author: Javier Fernández de Bobadilla
Publisher: American Mathematical Soc.
Published: 2005
Total Pages: 154
ISBN-13: 0821835939
DOWNLOAD EBOOK →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
Author: Greg Hjorth
Publisher: American Mathematical Soc.
Published: 2005
Total Pages: 126
ISBN-13: 0821837710
DOWNLOAD EBOOK →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.
Author: Yaozhong Hu
Publisher: American Mathematical Soc.
Published: 2005
Total Pages: 144
ISBN-13: 0821837044
DOWNLOAD EBOOK →A paper that studies two types of integral transformation associated with fractional Brownian motion. They are applied to construct approximation schemes for fractional Brownian motion by polygonal approximation of standard Brownian motion. This approximation is the best in the sense that it minimizes the mean square error.
Author: Philip L. Bowers
Publisher: American Mathematical Soc.
Published: 2004
Total Pages: 118
ISBN-13: 0821835238
DOWNLOAD EBOOK →Introduction Dessins d'enfants Discrete Dessins via circle packing Uniformizing Dessins A menagerie of Dessins d'enfants Computational issues Additional constructions Non-equilateral triangulations The discrete option Appendix: Implementation Bibliography.
Author: Jason Fulman
Publisher: American Mathematical Soc.
Published: 2005
Total Pages: 104
ISBN-13: 0821837060
DOWNLOAD EBOOK →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.
Author: Harold G. Dales
Publisher: American Mathematical Soc.
Published: 2005
Total Pages: 206
ISBN-13: 0821837745
DOWNLOAD EBOOK →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 $A""$.
Author: Ken'ichi Ōshika
Publisher: American Mathematical Soc.
Published: 2005
Total Pages: 136
ISBN-13: 0821837729
DOWNLOAD EBOOK →Ahlfors conjectured in 1964 that the limit set of every finitely generated Kleinian group either has Lebesgue measure $0$ or is the entire $S^2$. This title intends to prove that this conjecture is true for purely loxodromic Kleinian groups which are algebraic limits of geometrically finite groups.