02991nam 22004215a 450 991015193310332120091109150325.03-03719-564-910.4171/064(CKB)3710000000953844(CH-001817-3)103-091109(PPN)178155640(EXLCZ)99371000000095384420091109j20090808 fy 0engurnn|mmmmamaatxtrdacontentcrdamediacrrdacarrierLectures on Curves, Surfaces and Projective Varieties[electronic resource] A Classical View of Algebraic Geometry First corrected reprint, June 2012 /Mauro C. Beltrametti, Ettore Carletti, Dionisio Gallarati, Giacomo Monti BragadinZuerich, Switzerland European Mathematical Society Publishing House20091 online resource (506 pages)EMS Textbooks in Mathematics (ETB)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 of the last two years of an undergraduate program in mathematics. It contains some rather advanced topics suitable for specialized courses on 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.Algebraic geometrybicsscAlgebraic geometrymscAlgebraic geometryAlgebraic geometry14-xxmscBeltrametti Mauro C.58418Carletti EttoreGallarati DionisioMonti Bragadin Giacomoch0018173BOOK9910151933103321Lectures on Curves, Surfaces and Projective Varieties2565748UNINA