New Techniques In Resolution Of Singularities

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New Techniques In Resolution Of Singularities
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Author : Dan Abramovich
language : en
Publisher: Springer Nature
Release Date : 2023-09-14
New Techniques In Resolution Of Singularities written by Dan Abramovich and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-14 with Mathematics categories.
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.
Mordell Weil Lattices
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Author : Matthias Schütt
language : en
Publisher: Springer Nature
Release Date : 2019-10-17
Mordell Weil Lattices written by Matthias Schütt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-17 with Mathematics categories.
This book lays out the theory of Mordell–Weil lattices, a very powerful and influential tool at the crossroads of algebraic geometry and number theory, which offers many fruitful connections to other areas of mathematics. The book presents all the ingredients entering into the theory of Mordell–Weil lattices in detail, notably, relevant portions of lattice theory, elliptic curves, and algebraic surfaces. After defining Mordell–Weil lattices, the authors provide several applications in depth. They start with the classification of rational elliptic surfaces. Then a useful connection with Galois representations is discussed. By developing the notion of excellent families, the authors are able to design many Galois representations with given Galois groups such as the Weyl groups of E6, E7 and E8. They also explain a connection to the classical topic of the 27 lines on a cubic surface. Two chapters deal with elliptic K3 surfaces, a pulsating area of recent research activity which highlights many central properties of Mordell–Weil lattices. Finally, the book turns to the rank problem—one of the key motivations for the introduction of Mordell–Weil lattices. The authors present the state of the art of the rank problem for elliptic curves both over Q and over C(t) and work out applications to the sphere packing problem. Throughout, the book includes many instructive examples illustrating the theory.
Homological Methods In Commutative Algebra
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Author : Andrea Ferretti
language : en
Publisher: American Mathematical Society
Release Date : 2023-11-30
Homological Methods In Commutative Algebra written by Andrea Ferretti and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-30 with Mathematics categories.
This book develops the machinery of homological algebra and its applications to commutative rings and modules. It assumes familiarity with basic commutative algebra, for example, as covered in the author's book, Commutative Algebra. The first part of the book is an elementary but thorough exposition of the concepts of homological algebra, starting from categorical language up to the construction of derived functors and spectral sequences. A full proof of the celebrated Freyd-Mitchell theorem on the embeddings of small Abelian categories is included. The second part of the book is devoted to the application of these techniques in commutative algebra through the study of projective, injective, and flat modules, the construction of explicit resolutions via the Koszul complex, and the properties of regular sequences. The theory is then used to understand the properties of regular rings, Cohen-Macaulay rings and modules, Gorenstein rings and complete intersections. Overall, this book is a valuable resource for anyone interested in learning about homological algebra and its applications in commutative algebra. The clear and thorough presentation of the material, along with the many examples and exercises of varying difficulty, make it an excellent choice for self-study or as a reference for researchers.
Singularity Theory
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Author : Denis Chniot
language : en
Publisher: World Scientific
Release Date : 2007
Singularity Theory written by Denis Chniot and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
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.
Singularity Theory Dedicated To Jean Paul Brasselet On His 60th Birthday Proceedings Of The 2005 Marseille Singularity School And Conference
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Author : Jean-paul Brasselet
language : en
Publisher: World Scientific
Release Date : 2007-02-08
Singularity Theory Dedicated To Jean Paul Brasselet On His 60th Birthday Proceedings Of The 2005 Marseille Singularity School And Conference written by Jean-paul Brasselet and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-08 with Mathematics categories.
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.
Recent Trends In Science And Technology Rtst 2023
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Author : Dr. Sr. Shanta Joseph, Dr. Usha Shukla, Dr. Pramod Yadaw, Mrs. Mamta Kashyap, Dr. W.B. Gurnule
language : en
Publisher: Shashwat Publication
Release Date : 2024-05-29
Recent Trends In Science And Technology Rtst 2023 written by Dr. Sr. Shanta Joseph, Dr. Usha Shukla, Dr. Pramod Yadaw, Mrs. Mamta Kashyap, Dr. W.B. Gurnule and has been published by Shashwat Publication this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-29 with Biography & Autobiography categories.
International Seminar, Research Papers Proceeding on Recent Trends in Science and Technology (RTST-2023)
Resolution Of Singularities
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Author : Steven Dale Cutkosky
language : en
Publisher: American Mathematical Soc.
Release Date :
Resolution Of Singularities written by Steven Dale Cutkosky and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
"Besides explaining the tools needed for understanding resolutions, Cutkosky explains the history and ideas, providing 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 a 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."--BOOK JACKET.
Notices Of The American Mathematical Society
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Author : American Mathematical Society
language : en
Publisher:
Release Date : 1991
Notices Of The American Mathematical Society written by American Mathematical Society and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
Surveys On Recent Developments In Algebraic Geometry
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Author : Izzet Coskun
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-07-12
Surveys On Recent Developments In Algebraic Geometry written by Izzet Coskun and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-12 with Mathematics categories.
The algebraic geometry community has a tradition of running a summer research institute every ten years. During these influential meetings a large number of mathematicians from around the world convene to overview the developments of the past decade and to outline the most fundamental and far-reaching problems for the next. The meeting is preceded by a Bootcamp aimed at graduate students and young researchers. This volume collects ten surveys that grew out of the Bootcamp, held July 6–10, 2015, at University of Utah, Salt Lake City, Utah. These papers give succinct and thorough introductions to some of the most important and exciting developments in algebraic geometry in the last decade. Included are descriptions of the striking advances in the Minimal Model Program, moduli spaces, derived categories, Bridgeland stability, motivic homotopy theory, methods in characteristic and Hodge theory. Surveys contain many examples, exercises and open problems, which will make this volume an invaluable and enduring resource for researchers looking for new directions.
A Textbook Of Engineering Mathematics Part 2
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Author : Prof (Dr) Basant Kumar Singh
language : en
Publisher: Pen and Paper Academy
Release Date : 2025-03-31
A Textbook Of Engineering Mathematics Part 2 written by Prof (Dr) Basant Kumar Singh and has been published by Pen and Paper Academy this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-31 with Antiques & Collectibles categories.
Master the fundamental concepts of Ordinary Differential Equations, Partial Differential Equations, Fourier Series, Complex Variables, and Vector Calculus with this well-structured and student-friendly textbook. Designed specifically for B.Tech first-year students, this book provides clear explanations, step-by-step derivations, and practical applications to strengthen mathematical problem-solving skills. Key Features: ✅ Detailed Coverage – Covers essential topics like Second-Order Linear Differential Equations, Legendre Polynomials, Fourier Transforms, and Residue Theorem. ✅ Conceptual Clarity – Simplifies complex mathematical concepts with easy-to-follow explanations and examples. ✅ Real-World Applications – Demonstrates the practical relevance of mathematical theories in engineering. ✅ Problem-Solving Approach – Includes previous years’ exam questions to help students prepare effectively. ✅ Comprehensive Exercises – Offers a variety of solved and unsolved problems for practice. Perfect for engineering students, competitive exam aspirants, and mathematics enthusiasts, this book serves as an essential resource for mastering the mathematical foundations required for technical studies. Enhance your mathematical proficiency and excel in your exams with this indispensable guide!