Algebraic Spaces And Stacks
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| Author | : Martin Olsson |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 313 |
| Release | : 2016-05-13 |
| Genre | : Mathematics |
| ISBN | : 1470427982 |
This book is an introduction to the theory of algebraic spaces and stacks intended for graduate students and researchers familiar with algebraic geometry at the level of a first-year graduate course. The first several chapters are devoted to background material including chapters on Grothendieck topologies, descent, and fibered categories. Following this, the theory of algebraic spaces and stacks is developed. The last three chapters discuss more advanced topics including the Keel-Mori theorem on the existence of coarse moduli spaces, gerbes and Brauer groups, and various moduli stacks of curves. Numerous exercises are included in each chapter ranging from routine verifications to more difficult problems, and a glossary of necessary category theory is included as an appendix.
| Author | : Barbara Fantechi |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 354 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 0821842455 |
Presents an outline of Alexander Grothendieck's theories. This book discusses four main themes - descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. It is suitable for those working in algebraic geometry.
| Author | : Gerd Faltings |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 328 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 3662026325 |
A new and complete treatment of semi-abelian degenerations of abelian varieties, and their application to the construction of arithmetic compactifications of Siegel moduli space, with most of the results being published for the first time. Highlights of the book include a classification of semi-abelian schemes, construction of the toroidal and the minimal compactification over the integers, heights for abelian varieties over number fields, and Eichler integrals in several variables, together with a new approach to Siegel modular forms. A valuable source of reference for researchers and graduate students interested in algebraic geometry, Shimura varieties or diophantine geometry.
| Author | : Robert H. Dijkgraaf |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 570 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461242649 |
The moduli space Mg of curves of fixed genus g – that is, the algebraic variety that parametrizes all curves of genus g – is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory.
| Author | : Robin Hartshorne |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 511 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 1475738498 |
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 Eisenbud |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 265 |
| Release | : 2006-04-06 |
| Genre | : Mathematics |
| ISBN | : 0387226397 |
Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.
| Author | : Carles Casacuberta |
| Publisher | : Birkhäuser |
| Total Pages | : 630 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034882661 |
This is the second volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician.
| Author | : Bertrand Toën |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 242 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 0821840991 |
This is the second part of a series of papers called "HAG", devoted to developing the foundations of homotopical algebraic geometry. The authors start by defining and studying generalizations of standard notions of linear algebra in an abstract monoidal model category, such as derivations, étale and smooth morphisms, flat and projective modules, etc. They then use their theory of stacks over model categories to define a general notion of geometric stack over a base symmetric monoidal model category $C$, and prove that this notion satisfies the expected properties.
| Author | : David A. Cox |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 498 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 082182127X |
Mirror symmetry began when theoretical physicists made some astonishing predictions about rational curves on quintic hypersurfaces in four-dimensional projective space. Understanding the mathematics behind these predictions has been a substantial challenge. This book is the first completely comprehensive monograph on mirror symmetry, covering the original observations by the physicists through the most recent progress made to date. Subjects discussed include toric varieties, Hodge theory, Kahler geometry, moduli of stable maps, Calabi-Yau manifolds, quantum cohomology, Gromov-Witten invariants, and the mirror theorem. This title features: numerous examples worked out in detail; an appendix on mathematical physics; an exposition of the algebraic theory of Gromov-Witten invariants and quantum cohomology; and, a proof of the mirror theorem for the quintic threefold.
| Author | : Vincent Cossart |
| Publisher | : Springer Nature |
| Total Pages | : 258 |
| Release | : 2020-08-27 |
| Genre | : Mathematics |
| ISBN | : 3030526402 |
This book provides a rigorous and self-contained review of desingularization theory. Focusing on arbitrary dimensional schemes, it discusses the important concepts in full generality, complete with proofs, and includes an introduction to the basis of Hironaka’s Theory. The core of the book is a complete proof of desingularization of surfaces; despite being well-known, this result was no more than folklore for many years, with no existing references. Throughout the book there are numerous computations on standard bases, blowing ups and characteristic polyhedra, which will be a source of inspiration for experts exploring bigger dimensions. Beginners will also benefit from a section which presents some easily overlooked pathologies.
