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| Author | : Dan Abramovich |
| Publisher | : Springer Nature |
| Total Pages | : 345 |
| Release | : 2023-10-16 |
| Genre | : Mathematics |
| ISBN | : 3031321154 |
Download New Techniques in Resolution of Singularities Book in PDF, ePub and Kindle
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 | : János Kollár |
| Publisher | : Princeton University Press |
| Total Pages | : 215 |
| Release | : 2009-01-10 |
| Genre | : Mathematics |
| ISBN | : 1400827809 |
Download Lectures on Resolution of Singularities (AM-166) Book in PDF, ePub and Kindle
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 | : Steven Dale Cutkosky |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 198 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 0821835556 |
Download Resolution of Singularities Book in PDF, ePub and Kindle
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 | : Vincent Cossart |
| Publisher | : Springer |
| Total Pages | : 138 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540391258 |
Download Resolution of Surface Singularities Book in PDF, ePub and Kindle
| Author | : Javier Fernández de Bobadilla |
| Publisher | : Springer Nature |
| Total Pages | : 332 |
| Release | : 2021-05-27 |
| Genre | : Mathematics |
| ISBN | : 3030619583 |
Download Singularities and Their Interaction with Geometry and Low Dimensional Topology Book in PDF, ePub and Kindle
The book is a collection of surveys and original research articles concentrating on new perspectives and research directions at the crossroads of algebraic geometry, topology, and singularity theory. The papers, written by leading researchers working on various topics of the above fields, are the outcome of the “Némethi60: Geometry and Topology of Singularities” conference held at the Alfréd Rényi Institute of Mathematics in Budapest, from May 27 to 31, 2019. Both the conference and this resulting volume are in honor of Professor András Némethi, on the occasion of his 60th birthday, whose work plays a decisive and influential role in the interactions between the above fields. The book should serve as a valuable resource for graduate students and researchers to deepen the new perspectives, methods, and connections between geometry and topology regarding singularities.
| Author | : Antonio Campillo Lopez |
| Publisher | : |
| Total Pages | : 436 |
| Release | : 1995-01-26 |
| Genre | : |
| ISBN | : 9783034890212 |
Download Algebraic Geometry and Singularities Book in PDF, ePub and Kindle
The focus of this volume lies on singularity theory in algebraic geometry. It includes papers documenting recent and original developments and methods in subjects such as resolution of singularities, D-module theory, singularities of maps and geometry of curves. The papers originate from the Third International Conference on Algebraic Geometry held in La Rabida, Spain, in December 1991. Since then, the articles have undergone a meticulous process of refereeing and improvement, and they have been organized into a comprehensive account of the state of the art in this field.
| Author | : Antonio Campillo Lopez |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 448 |
| Release | : 1995-01-26 |
| Genre | : Mathematics |
| ISBN | : 9783764353346 |
Download Algebraic Geometry and Singularities Book in PDF, ePub and Kindle
The volume contains both general and research papers. Among the first ones are papers showing recent and original developments or methods in subjects such as resolution of singularities, D-module theory, singularities of maps and geometry of curves. The research papers deal on topics related to, or close to, those listed_above. The contributions are organized in three parts according to their contents. Part I presents a set of papers on resolution of singularities, a topic of renewed activity. It deals with important topics of current interest, such as canonical, algorithmic, combinatorial and graphical procedures (Villamayor, Oka, Marijmin), as well as special results on desingularization in characteristic p (Cossart, Moh), and connections between resolution and structure of the space of arcs through a singularity (Gonz81ez-Sprinberg-Lejeune-Jalabert). Part II contains a series of papers on the study~of singularities and its connections with differential systems and deformation or perturbation theo ries. Two expository papers (Maisonobe-Briam;on, :'vlebkhout) describe, in an algebro-geometric way, the interaction between singularities and D-module t.he ory including recent progress on Bernstein polynomials and Newton polygon techniques. Geometry of foliations (Henaut, Garcfa-Reguera), polar varieties and stratifications (Hajto) are also topics treated here. Two other papers (Wall, Greuel-Pfister) deal with quasihomogeneous singularities in the contexts of per turbations and moduli spaces. Globalization of deformations of singularities (de Jong) and determination of complex topology from the real one (~10nd) com plete this series of papers. Part III consists of papers on algebraic geometry of curves and surfaces.
| Author | : Jean-paul Brasselet |
| Publisher | : World Scientific |
| Total Pages | : 917 |
| Release | : 2007-01-16 |
| Genre | : Mathematics |
| ISBN | : 9814477044 |
Download Singularities In Geometry And Topology - Proceedings Of The Trieste Singularity Summer School And Workshop Book in PDF, ePub and Kindle
Singularity theory appears in numerous branches of mathematics, as well as in many emerging areas such as robotics, control theory, imaging, and various evolving areas in physics. The purpose of this proceedings volume is to cover recent developments in singularity theory and to introduce young researchers from developing countries to singularities in geometry and topology.The contributions discuss singularities in both complex and real geometry. As such, they provide a natural continuation of the previous school on singularities held at ICTP (1991), which is recognized as having had a major influence in the field.
| Author | : David Ellwood |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 353 |
| Release | : 2014-12-12 |
| Genre | : Mathematics |
| ISBN | : 0821889826 |
Download The Resolution of Singular Algebraic Varieties Book in PDF, ePub and Kindle
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 | : José Luis Cisneros Molina |
| Publisher | : Springer Nature |
| Total Pages | : 616 |
| Release | : 2020-10-24 |
| Genre | : Mathematics |
| ISBN | : 3030530612 |
Download Handbook of Geometry and Topology of Singularities I Book in PDF, ePub and Kindle
This volume consists of ten articles which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject. This is the first volume in a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.
