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| Author | : Christopher D. Hacon |
| Publisher | : Cambridge University Press |
| Total Pages | : 451 |
| Release | : 2015-01-15 |
| Genre | : Mathematics |
| ISBN | : 110764755X |
A comprehensive collection of expository articles on cutting-edge topics at the forefront of research in algebraic geometry.
| Author | : Izzet Coskun |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 370 |
| Release | : 2017-07-12 |
| Genre | : $K$-theory -- Higher algebraic $K$-theory -- $Q$- and plus-constructions |
| ISBN | : 1470435578 |
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.
| Author | : Lucia Caporaso |
| Publisher | : Cambridge University Press |
| Total Pages | : 437 |
| Release | : 2012-03-19 |
| Genre | : Mathematics |
| ISBN | : 052176825X |
This volume, based on a workshop by the MSRI, offers an overview of the state of the art in many areas of algebraic geometry.
| Author | : Matt Kerr |
| Publisher | : Cambridge University Press |
| Total Pages | : 533 |
| Release | : 2016-02-04 |
| Genre | : Mathematics |
| ISBN | : 110754629X |
Combines cutting-edge research and expository articles in Hodge theory. An essential reference for graduate students and researchers.
| Author | : Christopher Derek Hacon |
| Publisher | : |
| Total Pages | : |
| Release | : 2015 |
| Genre | : |
| ISBN | : 9781316212431 |
| Author | : Christopher D. Hacon |
| Publisher | : Cambridge University Press |
| Total Pages | : 451 |
| Release | : 2015-01-15 |
| Genre | : Mathematics |
| ISBN | : 131619583X |
Contemporary research in algebraic geometry is the focus of this collection, which presents articles on modern aspects of the subject. The list of topics covered is a roll-call of some of the most important and active themes in this thriving area of mathematics: the reader will find articles on birational geometry, vanishing theorems, complex geometry and Hodge theory, free resolutions and syzygies, derived categories, invariant theory, moduli spaces, and related topics, all written by leading experts. The articles, which have an expository flavour, present an overall picture of current research in algebraic geometry, making this book essential for researchers and graduate students. This volume is the outcome of the conference Recent Advances in Algebraic Geometry, held in Ann Arbor, Michigan, to honour Rob Lazarsfeld's many contributions to the subject on the occasion of his 60th birthday.
| Author | : Christopher Derek Hacon |
| Publisher | : |
| Total Pages | : 436 |
| Release | : 2015 |
| Genre | : Geometry, Algebraic |
| ISBN | : 9781316210611 |
A comprehensive collection of expository articles on cutting-edge topics at the forefront of research in algebraic geometry.
| Author | : Mihai Putinar |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 382 |
| Release | : 2008-12-10 |
| Genre | : Mathematics |
| ISBN | : 0387096868 |
Recent advances in both the theory and implementation of computational algebraic geometry have led to new, striking applications to a variety of fields of research. The articles in this volume highlight a range of these applications and provide introductory material for topics covered in the IMA workshops on "Optimization and Control" and "Applications in Biology, Dynamics, and Statistics" held during the IMA year on Applications of Algebraic Geometry. The articles related to optimization and control focus on burgeoning use of semidefinite programming and moment matrix techniques in computational real algebraic geometry. The new direction towards a systematic study of non-commutative real algebraic geometry is well represented in the volume. Other articles provide an overview of the way computational algebra is useful for analysis of contingency tables, reconstruction of phylogenetic trees, and in systems biology. The contributions collected in this volume are accessible to non-experts, self-contained and informative; they quickly move towards cutting edge research in these areas, and provide a wealth of open problems for future research.
| Author | : Ulrich Görtz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 615 |
| Release | : 2010-08-09 |
| Genre | : Mathematics |
| ISBN | : 3834897221 |
This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. Several examples from the realm of Hilbert modular surfaces and of determinantal varieties are used methodically to discuss the covered techniques. Thus the reader experiences that the further development of the theory yields an ever better understanding of these fascinating objects. The text is complemented by many exercises that serve to check the comprehension of the text, treat further examples, or give an outlook on further results. The volume at hand is an introduction to schemes. To get startet, it requires only basic knowledge in abstract algebra and topology. Essential facts from commutative algebra are assembled in an appendix. It will be complemented by a second volume on the cohomology of schemes.
| Author | : Bill Jacob |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 416 |
| Release | : 1994 |
| Genre | : Mathematics |
| ISBN | : 0821851543 |
The papers collected here present an up-to-date record of the current research developments in the fields of real algebraic geometry and quadratic forms. Articles range from the technical to the expository and there are also indications to new research directions.
