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Author | : David Mumford |
Publisher | : Princeton University Press |
Total Pages | : 220 |
Release | : 1966-08-21 |
Genre | : Mathematics |
ISBN | : 0691079935 |
Download Lectures on Curves on an Algebraic Surface Book in PDF, ePub and Kindle
These lectures, delivered by Professor Mumford at Harvard in 1963-1964, are devoted to a study of properties of families of algebraic curves, on a non-singular projective algebraic curve defined over an algebraically closed field of arbitrary characteristic. The methods and techniques of Grothendieck, which have so changed the character of algebraic geometry in recent years, are used systematically throughout. Thus the classical material is presented from a new viewpoint.
Author | : David Mumford |
Publisher | : Princeton University Press |
Total Pages | : 224 |
Release | : 1966-08-21 |
Genre | : Mathematics |
ISBN | : 9780691079936 |
Download Lectures on Curves on an Algebraic Surface Book in PDF, ePub and Kindle
These lectures, delivered by Professor Mumford at Harvard in 1963-1964, are devoted to a study of properties of families of algebraic curves, on a non-singular projective algebraic curve defined over an algebraically closed field of arbitrary characteristic. The methods and techniques of Grothendieck, which have so changed the character of algebraic geometry in recent years, are used systematically throughout. Thus the classical material is presented from a new viewpoint.
Author | : Mauro Beltrametti |
Publisher | : European Mathematical Society |
Total Pages | : 512 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 9783037190647 |
Download Lectures on Curves, Surfaces and Projective Varieties Book in PDF, ePub and Kindle
This book offers a wide-ranging introduction to algebraic geometry along classical lines. It consists of lectures on topics in classical algebraic geometry, including the basic properties of projective algebraic varieties, linear systems of hypersurfaces, algebraic curves (with special emphasis on rational curves), linear series on algebraic curves, Cremona transformations, rational surfaces, and notable examples of special varieties like the Segre, Grassmann, and Veronese varieties. An integral part and special feature of the presentation is the inclusion of many exercises, not easy to find in the literature and almost all with complete solutions. The text is aimed at students in the last two years of an undergraduate program in mathematics. It contains some rather advanced topics suitable for specialized courses at the advanced undergraduate or beginning graduate level, as well as interesting topics for a senior thesis. The prerequisites have been deliberately limited to basic elements of projective geometry and abstract algebra. Thus, for example, some knowledge of the geometry of subspaces and properties of fields is assumed. The book will be welcomed by teachers and students of algebraic geometry who are seeking a clear and panoramic path leading from the basic facts about linear subspaces, conics and quadrics to a systematic discussion of classical algebraic varieties and the tools needed to study them. The text provides a solid foundation for approaching more advanced and abstract literature.
Author | : David Mumford |
Publisher | : Princeton University Press |
Total Pages | : 212 |
Release | : 2016-03-02 |
Genre | : Mathematics |
ISBN | : 1400882060 |
Download Lectures on Curves on an Algebraic Surface. (AM-59), Volume 59 Book in PDF, ePub and Kindle
These lectures, delivered by Professor Mumford at Harvard in 1963-1964, are devoted to a study of properties of families of algebraic curves, on a non-singular projective algebraic curve defined over an algebraically closed field of arbitrary characteristic. The methods and techniques of Grothendieck, which have so changed the character of algebraic geometry in recent years, are used systematically throughout. Thus the classical material is presented from a new viewpoint.
Author | : David Mumford |
Publisher | : |
Total Pages | : 200 |
Release | : 1966 |
Genre | : Curves, Algebraic |
ISBN | : |
Download Lectures on Curves on an Algebraic Surface Book in PDF, ePub and Kindle
Author | : David Mumford |
Publisher | : |
Total Pages | : 200 |
Release | : 1985 |
Genre | : Curves, Algebraic |
ISBN | : |
Download Lectures on Curves on an Algebraic Surface Book in PDF, ePub and Kindle
Author | : Robert Friedman |
Publisher | : Springer Science & Business Media |
Total Pages | : 333 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461216885 |
Download Algebraic Surfaces and Holomorphic Vector Bundles Book in PDF, ePub and Kindle
A novel feature of the book is its integrated approach to algebraic surface theory and the study of vector bundle theory on both curves and surfaces. While the two subjects remain separate through the first few chapters, they become much more tightly interconnected as the book progresses. Thus vector bundles over curves are studied to understand ruled surfaces, and then reappear in the proof of Bogomolov's inequality for stable bundles, which is itself applied to study canonical embeddings of surfaces via Reider's method. Similarly, ruled and elliptic surfaces are discussed in detail, before the geometry of vector bundles over such surfaces is analysed. Many of the results on vector bundles appear for the first time in book form, backed by many examples, both of surfaces and vector bundles, and over 100 exercises forming an integral part of the text. Aimed at graduates with a thorough first-year course in algebraic geometry, as well as more advanced students and researchers in the areas of algebraic geometry, gauge theory, or 4-manifold topology, many of the results on vector bundles will also be of interest to physicists studying string theory.
Author | : Otto Forster |
Publisher | : Springer Science & Business Media |
Total Pages | : 262 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461259614 |
Download Lectures on Riemann Surfaces Book in PDF, ePub and Kindle
This book grew out of lectures on Riemann surfaces given by Otto Forster at the universities of Munich, Regensburg, and Münster. It provides a concise modern introduction to this rewarding subject, as well as presenting methods used in the study of complex manifolds in the special case of complex dimension one. From the reviews: "This book deserves very serious consideration as a text for anyone contemplating giving a course on Riemann surfaces."—-MATHEMATICAL REVIEWS
Author | : Phillip A. Griffiths |
Publisher | : American Mathematical Soc. |
Total Pages | : 225 |
Release | : 1989 |
Genre | : Mathematics |
ISBN | : 9780821845370 |
Download Introduction to Algebraic Curves Book in PDF, ePub and Kindle
This book differs from a number of recent books on this subject in that it combines analytic and geometric methods at the outset, so that the reader can grasp the basic results of the subject. Although such modern techniques of sheaf theory, cohomology, and commutative algebra are not covered here, the book provides a solid foundation to proceed to more advanced texts in general algebraic geometry, complex manifolds, and Riemann surfaces, as well as algebraic curves. Containing numerous exercises this book would make an excellent introductory text.
Author | : Hiraku Nakajima |
Publisher | : American Mathematical Soc. |
Total Pages | : 146 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 0821819569 |
Download Lectures on Hilbert Schemes of Points on Surfaces Book in PDF, ePub and Kindle
It has been realized that Hilbert schemes originally studied in algebraic geometry are closely related to several branches of mathematics, such as singularities, symplectic geometry, representation theory - even theoretical physics. This book reflects this feature of Hilbert schemes.