New Techniques in Resolution of Singularities PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download New Techniques in Resolution of Singularities PDF full book. Access full book title New Techniques in Resolution of Singularities by Dan Abramovich. Download full books in PDF and EPUB format.
Author: Dan Abramovich
Publisher: Springer Nature
ISBN: 3031321154
Category : Mathematics
Languages : en
Pages : 345
Get Book Here
Book Description
Resolution of singularities is notorious as a difficult topic within algebraic geometry. Recent work, aiming at resolution of families and semistable reduction, infused the subject with logarithmic geometry and algebraic stacks, two techniques essential for the current theory of moduli spaces. As a byproduct a short, a simple and efficient functorial resolution procedure in characteristic 0 using just algebraic stacks was produced. The goals of the book, the result of an Oberwolfach Seminar, are to introduce readers to explicit techniques of resolution of singularities with access to computer implementations, introduce readers to the theories of algebraic stacks and logarithmic structures, and to resolution in families and semistable reduction methods.
Author: Dan Abramovich
Publisher: Springer Nature
ISBN: 3031321154
Category : Mathematics
Languages : en
Pages : 345
Get Book Here
Book Description
Resolution of singularities is notorious as a difficult topic within algebraic geometry. Recent work, aiming at resolution of families and semistable reduction, infused the subject with logarithmic geometry and algebraic stacks, two techniques essential for the current theory of moduli spaces. As a byproduct a short, a simple and efficient functorial resolution procedure in characteristic 0 using just algebraic stacks was produced. The goals of the book, the result of an Oberwolfach Seminar, are to introduce readers to explicit techniques of resolution of singularities with access to computer implementations, introduce readers to the theories of algebraic stacks and logarithmic structures, and to resolution in families and semistable reduction methods.
Author: Steven Dale Cutkosky
Publisher: American Mathematical Soc.
ISBN: 0821835556
Category : Mathematics
Languages : en
Pages : 198
Get Book Here
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: János Kollár
Publisher: Princeton University Press
ISBN: 1400827809
Category : Mathematics
Languages : en
Pages : 215
Get Book Here
Book Description
Resolution of singularities is a powerful and frequently used tool in algebraic geometry. In this book, János Kollár provides a comprehensive treatment of the characteristic 0 case. He describes more than a dozen proofs for curves, many based on the original papers of Newton, Riemann, and Noether. Kollár goes back to the original sources and presents them in a modern context. He addresses three methods for surfaces, and gives a self-contained and entirely elementary proof of a strong and functorial resolution in all dimensions. Based on a series of lectures at Princeton University and written in an informal yet lucid style, this book is aimed at readers who are interested in both the historical roots of the modern methods and in a simple and transparent proof of this important theorem.
Author: Joe Harris
Publisher: Montréal : Presses de l'Université de Montréal
ISBN: 9782760606036
Category : Courbes algébriques
Languages : en
Pages : 138
Get Book Here
Book Description
Author: Sumio Watanabe
Publisher: Cambridge University Press
ISBN: 0521864674
Category : Computers
Languages : en
Pages : 295
Get Book Here
Book Description
Sure to be influential, Watanabe's book lays the foundations for the use of algebraic geometry in statistical learning theory. Many models/machines are singular: mixture models, neural networks, HMMs, Bayesian networks, stochastic context-free grammars are major examples. The theory achieved here underpins accurate estimation techniques in the presence of singularities.
Author: Robin Hartshorne
Publisher: Springer Science & Business Media
ISBN: 1475738498
Category : Mathematics
Languages : en
Pages : 511
Get Book Here
Book Description
An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.
Author: David Ellwood
Publisher: American Mathematical Soc.
ISBN: 0821889826
Category : Mathematics
Languages : en
Pages : 353
Get Book Here
Book Description
Resolution of Singularities has long been considered as being a difficult to access area of mathematics. The more systematic and simpler proofs that have appeared in the last few years in zero characteristic now give us a much better understanding of singularities. They reveal the aesthetics of both the logical structure of the proof and the various methods used in it. The present volume is intended for readers who are not yet experts but always wondered about the intricacies of resolution. As such, it provides a gentle and quite comprehensive introduction to this amazing field. The book may tempt the reader to enter more deeply into a topic where many mysteries--especially the positive characteristic case--await to be disclosed. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
Author: Marcos Marino
Publisher: Springer
ISBN: 3540798145
Category : Mathematics
Languages : en
Pages : 219
Get Book Here
Book Description
Starting in the middle of the 80s, there has been a growing and fruitful interaction between algebraic geometry and certain areas of theoretical high-energy physics, especially the various versions of string theory. Physical heuristics have provided inspiration for new mathematical definitions (such as that of Gromov-Witten invariants) leading in turn to the solution of problems in enumerative geometry. Conversely, the availability of mathematically rigorous definitions and theorems has benefited the physics research by providing the required evidence in fields where experimental testing seems problematic. The aim of this volume, a result of the CIME Summer School held in Cetraro, Italy, in 2005, is to cover part of the most recent and interesting findings in this subject.
Author: C. T. C. Wall
Publisher: Cambridge University Press
ISBN: 9780521547741
Category : Mathematics
Languages : en
Pages : 386
Get Book Here
Book Description
Publisher Description
Author: Clay Mathematics Institute. Summer School
Publisher: American Mathematical Soc.
ISBN: 9780821837153
Category : Mathematics
Languages : en
Pages : 396
Get Book Here
Book Description
Contains selection of expository and research article by lecturers at the school. Highlights current interests of researchers working at the interface between string theory and algebraic supergravity, supersymmetry, D-branes, the McKay correspondence andFourer-Mukai transform.
