Buch, Englisch, Band 129, 327 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 588 g
Reihe: La Matematica per il 3+2
Buch, Englisch, Band 129, 327 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 588 g
Reihe: La Matematica per il 3+2
ISBN: 978-3-030-71020-0
Verlag: Springer International Publishing
The approach in this book is purely algebraic. The main tool is commutative algebra, from which the needed results are recalled, in most cases with proofs. The prerequisites consist of the knowledge of basics in affine and projective geometry, basic algebraic concepts regarding rings, modules, fields, linear algebra, basic notions in the theory of categories, and some elementary point–set topology.
This book can be used as a textbook for an undergraduate course in algebraic geometry. The users of the book are not necessarily intended to become algebraic geometers but may be interested students or researchers who want to have a first smattering in the topic.
The book contains several exercises, in which there are more examples and parts of the theory that are not fully developed in the text. Of some exercises, there are solutions at the end of each chapter.
Zielgruppe
Upper undergraduate
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
1 Affine and projective algebraic sets.- 2 Basic notions of elimination theory and applications.- 3 Zariski closed subsets and ideals in the polynomials ring.- 4 Some topological properties.- 5 Regular and rational functions.- 6 Morphisms.- 7 Rational maps.- 8 Product of varieties.- 9 More on elimination theory.- 10 Finite morphisms.- 11 Dimension.- 12 The Cayley form.- 13 Grassmannians.- 14 Smooth and singular points.- 15 Power series.- 16 A ne plane curves.- 17 Projective plane curves.- 18 Resolution of singularities of curves.- 19 Divisors, linear equivalence, linear series.- 20 The Riemann-Roch Theorem.