Lectures on Surfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Surfaces write by A. B. Katok. This book was released on 2008. Lectures on Surfaces available in PDF, EPUB and Kindle. Surfaces are among the most common and easily visualized mathematical objects, and their study brings into focus fundamental ideas, concepts, and methods from geometry, topology, complex analysis, Morse theory, and group theory. This book introduces many of the principal actors - the round sphere, flat torus, Mobius strip, and Klein bottle.
Lectures on Riemann Surfaces
Lectures on Riemann Surfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Riemann Surfaces write by Otto Forster. This book was released on 2012-12-06. Lectures on Riemann Surfaces available 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
Lectures on K3 Surfaces
Lectures on K3 Surfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on K3 Surfaces write by Daniel Huybrechts. This book was released on 2016-09-26. Lectures on K3 Surfaces available in PDF, EPUB and Kindle. K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi–Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs, such as the proof of the Tate conjecture for K3 surfaces and structural results on Chow groups. Powerful general techniques are introduced to study the many facets of K3 surfaces, including arithmetic, homological, and differential geometric aspects. In this context, the book covers Hodge structures, moduli spaces, periods, derived categories, birational techniques, Chow rings, and deformation theory. Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin–Tate, are discussed in general and for K3 surfaces in particular, and each chapter ends with questions and open problems. Based on lectures at the advanced graduate level, this book is suitable for courses and as a reference for researchers.
Lectures on Curves, Surfaces and Projective Varieties
Lectures on Curves, Surfaces and Projective Varieties - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Curves, Surfaces and Projective Varieties write by Mauro Beltrametti. This book was released on 2009. Lectures on Curves, Surfaces and Projective Varieties available 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.
Lectures on Riemann Surfaces
Lectures on Riemann Surfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Riemann Surfaces write by Robert C. Gunning. This book was released on 2015-03-08. Lectures on Riemann Surfaces available in PDF, EPUB and Kindle. A sequel to Lectures on Riemann Surfaces (Mathematical Notes, 1966), this volume continues the discussion of the dimensions of spaces of holomorphic cross-sections of complex line bundles over compact Riemann surfaces. Whereas the earlier treatment was limited to results obtainable chiefly by one-dimensional methods, the more detailed analysis presented here requires the use of various properties of Jacobi varieties and of symmetric products of Riemann surfaces, and so serves as a further introduction to these topics as well. The first chapter consists of a rather explicit description of a canonical basis for the Abelian differentials on a marked Riemann surface, and of the description of the canonical meromorphic differentials and the prime function of a marked Riemann surface. Chapter 2 treats Jacobi varieties of compact Riemann surfaces and various subvarieties that arise in determining the dimensions of spaces of holomorphic cross-sections of complex line bundles. In Chapter 3, the author discusses the relations between Jacobi varieties and symmetric products of Riemann surfaces relevant to the determination of dimensions of spaces of holomorphic cross-sections of complex line bundles. The final chapter derives Torelli's theorem following A. Weil, but in an analytical context. Originally published in 1973. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
