Weyl Groups and Birational Transformations among Minimal Models PDF Download
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Author: Kenji Matsuki
Publisher: American Mathematical Soc.
ISBN: 0821803417
Category : Mathematics
Languages : en
Pages : 146
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Book Description
In this paper we provide a unified way of looking at the apparently sporadic Weyl groups connected with the classical geometry of surfaces, namely those with 1) the rational double points, 2) the Picard groups of Del Pezzo surfaces, 3) the Kodaira-type degenerations of elliptic curves, and 4) the Picard-Lefschetz reflections of [italic]K3-surfaces, by putting them together into the picture of 3-dimensional birational geometry in the realm of the recently established Minimal Model Theory for 3-folds.
Author: Kenji Matsuki
Publisher: American Mathematical Soc.
ISBN: 0821803417
Category : Mathematics
Languages : en
Pages : 146
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Book Description
In this paper we provide a unified way of looking at the apparently sporadic Weyl groups connected with the classical geometry of surfaces, namely those with 1) the rational double points, 2) the Picard groups of Del Pezzo surfaces, 3) the Kodaira-type degenerations of elliptic curves, and 4) the Picard-Lefschetz reflections of [italic]K3-surfaces, by putting them together into the picture of 3-dimensional birational geometry in the realm of the recently established Minimal Model Theory for 3-folds.
Author: Kenji Matsuki
Publisher:
ISBN: 9781470401368
Category : Surfaces, Algebraic
Languages : en
Pages : 133
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Book Description
Author: Michael A. Dritschel
Publisher: American Mathematical Soc.
ISBN: 0821806513
Category : Mathematics
Languages : en
Pages : 77
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Book Description
This memoir initiates a model theory-based study of the numerical radius norm. Guided by the abstract model theory of Jim Agler, the authors propose a decomposition for operators that is particularly useful in understanding their properties with respect to the numerical radius norm. Of the topics amenable to investigation with these tools, the following are presented: a complete description of the linear extreme points of the non-matrix (numerical radius) unit ball; several equivalent characterizations of matricial extremals in the unit ball, that is, those members which do not allow a nontrivial extension remaining in the unit ball; and applications to numerical ranges of matrices, including a complete parameterization of all matrices whose numerical ranges are closed disks.
Author: Eldar Straume
Publisher: American Mathematical Soc.
ISBN: 082180409X
Category : Mathematics
Languages : en
Pages : 106
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Book Description
The cohomogeneity of a transformation group ([italic capitals]G, X) is, by definition, the dimension of its orbit space, [italic]c = dim [italic capitals]X, G. By enlarging this simple numerical invariant, but suitably restricted, one gradually increases the complexity of orbit structures of transformation groups. This is a natural program for classical space forms, which traditionally constitute the first canonical family of testing spaces, due to their unique combination of topological simplicity and abundance in varieties of compact differentiable transformation groups.
Author: Eldar Straume
Publisher: American Mathematical Soc.
ISBN: 0821804839
Category : Mathematics
Languages : en
Pages : 90
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Book Description
The cohomogeneity of a transformation group ([italic capitals]G, X) is, by definition, the dimension of its orbit space, [italic]c = dim [italic capitals]X, G. We are concerned with the classification of differentiable compact connected Lie transformation groups on (homology) spheres, with [italic]c [less than or equal to symbol] 2, and the main results are summarized in five theorems, A, B, C, D, and E in part I. This paper is part II of the project, and addresses theorems D and E. D examines the orthogonal model from theorem A and orbit structures, while theorem E addresses the existence of "exotic" [italic capital]G-spheres.
Author: Friedrich Tomi
Publisher: American Mathematical Soc.
ISBN: 0821803522
Category : Mathematics
Languages : en
Pages : 90
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Book Description
In this paper we formulate and prove an index theorem for minimal surfaces of higher topological type spanning one boundary contour. Our techniques carry over to surfaces with several boundary contours as well as to unoriented surfaces.
Author: Masayuki Kawakita
Publisher: Cambridge University Press
ISBN: 1108844235
Category : Mathematics
Languages : en
Pages : 503
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Book Description
A detailed treatment of the explicit aspects of the birational geometry of algebraic threefolds arising from the minimal model program.
Author: David Ginzburg
Publisher: American Mathematical Soc.
ISBN: 0821805436
Category : Mathematics
Languages : en
Pages : 233
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Book Description
In this book, the authors establish global Rankin Selberg integrals which determine the standard [italic capital]L function for the group [italic capitals]GL[subscript italic]r x [italic capital]Gʹ, where [italic capital]Gʹ is an isometry group of a nondegenerate symmetric form. The class of automorphic representations considered here is for any pair [capital Greek]Pi1 [otimes/dyadic/Kronecker/tensor product symbol] [capital Greek]Pi2 where [capital Greek]Pi1 is generic cuspidal for [italic capitals]GL[subscript italic]r([italic capital]A) and [capital Greek]Pi2 is cuspidal for [italic capital]Gʹ([italic capital]A). The construction of these [italic capital]L functions involves the use of certain new "models" of local representations; these models generalize the usual generic models. The authors also computer local unramified factors in a new way using geometric ideas.
Author: Serguei Germanovich Bobkov
Publisher: American Mathematical Soc.
ISBN: 0821806424
Category : Art
Languages : en
Pages : 127
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Book Description
For Borel probability measures on metric spaces, this text studies the interplay between isoperimetric and Sobolev-type inequalities. In particular the question of finding optimal constants via isoperimetric quantities is explored. Also given are necessary and sufficient conditions for the equivalence between the extremality of some sets in the isoperimetric problem and the validity of some analytic inequalities. The book devotes much attention to: the probability distributions on the real line; the normalized Lebesgue measure on the Euclidean sheres; and the canonical Gaussian measure on the Euclidean space.
Author: Robin Hartshorne
Publisher: American Mathematical Soc.
ISBN: 0821806483
Category : Mathematics
Languages : en
Pages : 111
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Book Description
Content Description #"November 1997, volume 130, number 617 (first of 4 numbers)."#On t.p. "P" is blackboard bold.#Includes bibliographical references.
