Author: Marcel Berger Genre: Mathematics Publisher: Springer Science & Business Media ISBN: 3540170154 Book Pages: 406 Format: PDF, ePub & Mobi
This is the second of a two-volume textbook that provides a very readable and lively presentation of large parts of geometry in the classical sense. For each topic the author presents a theorem that is esthetically pleasing and easily stated, although the proof may be quite hard and concealed. Yet another strong trait of the book is that it provides a comprehensive and unified reference source for the field of geometry in the full breadth of its subfields and ramifications.
Author: E.B. Vinberg Genre: Mathematics Publisher: Springer Science & Business Media ISBN: 9783662029015 Book Pages: 256 Format: PDF, ePub & Mobi
A very clear account of the subject from the viewpoints of elementary geometry, Riemannian geometry and group theory – a book with no rival in the literature. Mostly accessible to first-year students in mathematics, the book also includes very recent results which will be of interest to researchers in this field.
Author: 健爾·上野 Genre: Mathematics Publisher: American Mathematical Soc. ISBN: 0821813579 Book Pages: 184 Format: PDF, ePub & Mobi
Modern algebraic geometry is built upon two fundamental notions: schemes and sheaves. The theory of schemes is presented in the first part of this book (Algebraic Geometry 1: From Algebraic Varieties to Schemes, AMS, 1999, Translations of Mathematical Monographs, Volume 185). In the present book, the author turns to the theory of sheaves and their cohomology. Loosely speaking, a sheaf is a way of keeping track of local information defined on a topological space, such as the local algebraic functions on an algebraic manifold or the local sections of a vector bundle. Sheaf cohomology is a primary tool in understanding sheaves and using them to study properties of the corresponding manifolds. The text covers the important topics of the theory of sheaves on algebraic varieties, including types of sheaves and the fundamental operations on them, such as coherent and quasicoherent sheaves, direct and inverse images, behavior of sheaves under proper and projective morphisms, and Cech cohomology. The book contains numerous problems and exercises with solutions. It would be an excellent text for the second part of a course in algebraic geometry.
Author: Igor R. Shafarevich Genre: Mathematics Publisher: Springer ISBN: 9783642579561 Book Pages: 270 Format: PDF, ePub & Mobi
The second volume of Shafarevich's introductory book on algebraic geometry focuses on schemes, complex algebraic varieties and complex manifolds. As with first volume the author has revised the text and added new material. Although the material is more advanced than in Volume 1 the algebraic apparatus is kept to a minimum making the book accessible to non-specialists. It can be read independently of the first volume and is suitable for beginning graduate students.
Author: I.R. Shafarevich Genre: Mathematics Publisher: Springer Science & Business Media ISBN: 9783642609251 Book Pages: 264 Format: PDF, ePub & Mobi
This two-part volume contains numerous examples and insights on various topics. The authors have taken pains to present the material rigorously and coherently. This book will be immensely useful to mathematicians and graduate students working in algebraic geometry, arithmetic algebraic geometry, complex analysis and related fields.
Author: R.K. Lazarsfeld Genre: Mathematics Publisher: Springer Science & Business Media ISBN: 354022534X Book Pages: 385 Format: PDF, ePub & Mobi
This two volume work on "Positivity in Algebraic Geometry" contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity. Topics in Volume I include ample line bundles and linear series on a projective variety, the classical theorems of Lefschetz and Bertini and their modern outgrowths, vanishing theorems, and local positivity. Volume II begins with a survey of positivity for vector bundles, and moves on to a systematic development of the theory of multiplier ideals and their applications. A good deal of this material has not previously appeared in book form, and substantial parts are worked out here in detail for the first time. At least a third of the book is devoted to concrete examples, applications, and pointers to further developments. Whereas Volume I is more elementary, the present Volume II is more at the research level and somewhat more specialized. Both volumes are also available as hardcover edition as Vols. 48 and 49 in the series "Ergebnisse der Mathematik und ihrer Grenzgebiete".
Author: Sergey Novikov Genre: Education Publisher: American Mathematical Soc. ISBN: 9781470455927 Book Pages: 480 Format: PDF, ePub & Mobi
This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.