Monomialization of Morphisms from 3-Folds to Surfaces PDF Download
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Author: Steven D. Cutkosky
Publisher: Springer
ISBN: 3540480307
Category : Mathematics
Languages : en
Pages : 245
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Book Description
A morphism of algebraic varieties (over a field characteristic 0) is monomial if it can locally be represented in e'tale neighborhoods by a pure monomial mappings. The book gives proof that a dominant morphism from a nonsingular 3-fold X to a surface S can be monomialized by performing sequences of blowups of nonsingular subvarieties of X and S. The construction is very explicit and uses techniques from resolution of singularities. A research monograph in algebraic geometry, it addresses researchers and graduate students.
Author: Steven D. Cutkosky
Publisher: Springer
ISBN: 3540480307
Category : Mathematics
Languages : en
Pages : 245
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Book Description
A morphism of algebraic varieties (over a field characteristic 0) is monomial if it can locally be represented in e'tale neighborhoods by a pure monomial mappings. The book gives proof that a dominant morphism from a nonsingular 3-fold X to a surface S can be monomialized by performing sequences of blowups of nonsingular subvarieties of X and S. The construction is very explicit and uses techniques from resolution of singularities. A research monograph in algebraic geometry, it addresses researchers and graduate students.
Author: Olga S. Kashcheyeva
Publisher:
ISBN:
Category : Equivalence classes (Set theory)
Languages : en
Pages : 202
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Book Description
Monomialization of morphisms is the problem of transforming a mapping into a monomial mapping by blowing up a chain of nonsingular subvarieties in its domain and image. The notion of a strongly prepared morphism, a morphism with some local properties, was first introduced by S.D. Cutkosky in his paper on monomialization of morphisms from 3-folds to surfaces. As an intermediate result it was proved that after performing a finite sequence of blowups one can make every dominant morphism from a 3-fold to a surface strongly prepared. The similar result for higher dimensions is unknown. We prove that strongly prepared morphisms from n-folds to surfaces can be monomialized.
Author: Steven Dale Cutkosky
Publisher: American Mathematical Soc.
ISBN: 0821839985
Category : Mathematics
Languages : en
Pages : 234
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Book Description
This book contains a proof that a dominant morphism from a 3-fold $X$ to a variety $Y$ can be made toroidal by blowing up in the target and domain. We give applications to factorization of birational morphisms of 3-folds.
Author: Franz-Viktor Kuhlmann
Publisher: American Mathematical Soc.
ISBN: 9780821871393
Category : Mathematics
Languages : en
Pages : 470
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Book Description
This book is the first of two proceedings volumes stemming from the International Conference and Workshop on Valuation Theory held at the University of Saskatchewan (Saskatoon, SK, Canada). Valuation theory arose in the early part of the twentieth century in connection with number theory and has many important applications to geometry and analysis: the classical application to the study of algebraic curves and to Dedekind and Prufer domains; the close connection to the famousresolution of the singularities problem; the study of the absolute Galois group of a field; the connection between ordering, valuations, and quadratic forms over a formally real field; the application to real algebraic geometry; the study of noncommutative rings; etc. The special feature of this book isits focus on current applications of valuation theory to this broad range of topics. Also included is a paper on the history of valuation theory. The book is suitable for graduate students and research mathematicians working in algebra, algebraic geometry, number theory, and mathematical logic.
Author: Jürgen Herzog
Publisher: Springer Science & Business Media
ISBN: 9400710925
Category : Mathematics
Languages : en
Pages : 277
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Book Description
Proceedings of the NATO Advanced Research Workshop, held in Sinaia, Romania, 17-22 September 2002
Author: Steven Dale Cutkosky
Publisher: American Mathematical Soc.
ISBN: 0821835556
Category : Mathematics
Languages : en
Pages : 198
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Book Description
The notion of singularity is basic to mathematics. In algebraic geometry, the resolution of singularities by simple algebraic mappings is truly a fundamental problem. It has a complete solution in characteristic zero and partial solutions in arbitrary characteristic. The resolution of singularities in characteristic zero is a key result used in many subjects besides algebraic geometry, such as differential equations, dynamical systems, number theory, the theory of $\mathcal{D}$-modules, topology, and mathematical physics. This book is a rigorous, but instructional, look at resolutions. A simplified proof, based on canonical resolutions, is given for characteristic zero. There are several proofs given for resolution of curves and surfaces in characteristic zero and arbitrary characteristic. Besides explaining the tools needed for understanding resolutions, Cutkosky explains the history and ideas, providing valuable insight and intuition for the novice (or expert). There are many examples and exercises throughout the text. The book is suitable for a second course on an exciting topic in algebraic geometry. A core course on resolutions is contained in Chapters 2 through 6. Additional topics are covered in the final chapters. The prerequisite is a course covering the basic notions of schemes and sheaves.
Author: K. Kiyek
Publisher: Springer Science & Business Media
ISBN: 1402020295
Category : Mathematics
Languages : en
Pages : 506
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Book Description
The Curves The Point of View of Max Noether Probably the oldest references to the problem of resolution of singularities are found in Max Noether's works on plane curves [cf. [148], [149]]. And probably the origin of the problem was to have a formula to compute the genus of a plane curve. The genus is the most useful birational invariant of a curve in classical projective geometry. It was long known that, for a plane curve of degree n having l m ordinary singular points with respective multiplicities ri, i E {1, . . . , m}, the genus p of the curve is given by the formula = (n - l)(n - 2) _ ~ "r. (r. _ 1) P 2 2 L. . ,. •• . Of course, the problem now arises: how to compute the genus of a plane curve having some non-ordinary singularities. This leads to the natural question: can we birationally transform any (singular) plane curve into another one having only ordinary singularities? The answer is positive. Let us give a flavor (without proofs) 2 on how Noether did it • To solve the problem, it is enough to consider a special kind of Cremona trans formations, namely quadratic transformations of the projective plane. Let ~ be a linear system of conics with three non-collinear base points r = {Ao, AI, A }, 2 and take a projective frame of the type {Ao, AI, A ; U}.
Author: Jean-paul Brasselet
Publisher: World Scientific
ISBN: 9814476390
Category : Mathematics
Languages : en
Pages : 1083
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Book Description
The Singularity School and Conference took place in Luminy, Marseille, from January 24th to February 25th 2005. More than 180 mathematicians from over 30 countries converged to discuss recent developments in singularity theory.The volume contains the elementary and advanced courses conducted by singularities specialists during the conference, general lectures on singularity theory, and lectures on applications of the theory to various domains. The subjects range from geometry and topology of singularities, through real and complex singularities, to applications of singularities.
Author: Denis Cheniot
Publisher: World Scientific
ISBN: 9812707492
Category : Mathematics
Languages : en
Pages : 1083
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Book Description
The Singularity School and Conference took place in Luminy, Marseille, from January 24th to February 25th 2005. More than 180 mathematicians from over 30 countries converged to discuss recent developments in singularity theory. The volume contains the elementary and advanced courses conducted by singularities specialists during the conference, general lectures on singularity theory, and lectures on applications of the theory to various domains. The subjects range from geometry and topology of singularities, through real and complex singularities, to applications of singularities.
Author: Yasuyuki Kachi
Publisher: American Mathematical Soc.
ISBN: 0821834010
Category : Mathematics
Languages : en
Pages : 186
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Book Description
This proceedings volume resulted from the John H. Barrett Memorial Lecture Series held at the University of Tennessee (Knoxville). The articles reflect recent developments in algebraic geometry. It is suitable for graduate students and researchers interested in algebra and algebraic geometry.
