![]() ![]() Nice results were obtained in algebraic geometry over commutative monoids with cancellation 50, 76, 77. Of some exercises, there are solutions at the end of each chapter. Algebraic geometry over algebraic structures is also being developed for algebraic structures other than groups. The book contains several exercises, in which there are more examples and parts of the theory that are not fully developed in the text. 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. This book can be used as a textbook for an undergraduate course in algebraic geometry. ![]() 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. Chapter 2: AFFINE ALGEBRAIC GEOMETRY 2.1 Rings and Modules 2.2 The Zariski Topology 2.3 Some Afne Varieties 2.4 The Nullstellensatz 2.5 The Spectrum of a Finite-type Domain 2.6 Morphisms of Afne Varieties 2.7 Finite Group Actions Chapter 3: PROJECTIVE ALGEBRAIC GEOMETRY 3.1 Projective Varieties 3.2 Homogeneous Ideals 3. The main tool is commutative algebra, from which the needed results are recalled, in most cases with proofs. The approach in this book is purely algebraic. The second part is devoted to the theory of curves: local properties, affine and projective plane curves, resolution of singularities, linear equivalence of divisors and linear series, Riemann–Roch and Riemann–Hurwitz Theorems. The first is devoted to an introduction to basic concepts in algebraic geometry: affine and projective varieties, some of their main attributes and examples. ![]()
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