FIRST COURSE IN ALGEBRAIC GEOMETRY AND ALGEBRAIC VARIETIES

This book provides a gentle introduction to the foundations of Algebraic Geometry, starting from computational topics (ideals and homogeneous ideals, zero loci of ideals) up to increasingly intrinsic and abstract arguments, such as 'Algebraic Varieties', whose natural continuation is a more advanced course on the theory of schemes, vector bundles, and sheaf-cohomology. Valuable to students studying Algebraic Geometry and Geometry, this title contains around 60 exercises (with solutions) to help students thoroughly understand the theories introduced in the book. Proofs of the results are carried out in full detail. Many examples are discussed in order to reinforce the understanding of both the theoretical elements and their consequences, as well as the possible applications of the material. Contents: Preface About the Author Acknowledgments Basics on Commutative Algebra Algebraic Affine Sets Algebraic Projective Sets Topological Properties and Algebraic Varieties Regular and Rational Functions on Algebraic Varieties Morphisms of Algebraic Varieties Products of Algebraic Varieties Rational Maps of Algebraic Varieties Completeness of Projective Varieties Dimension of Algebraic Varieties Fiber-Dimension: Semicontinuity Tangent Spaces: Smoothness of Algebraic Varieties Solutions to Exercises Bibliography Index Readership: Advanced undergraduate students (specifically in their 3rd year of undergraduate study or their 1st year of postgraduate study) in the field of Algebraic Geometry; advanced Bachelor courses in Geometry or first courses Geometry during postgraduate study. 'The readers are taken by the hand and shown introductory and fundamental notions of Algebraic Geometry. The problems at the end of each chapter are helpful for ensuring a better understanding and for further practice of the concepts dealt with in the textbook. The clarity of presentation makes the book suitable and versatile in different contexts, not only — as one might assume at first sight — for the courses of the three-year degree in Mathematics.' - Gilberto BiniProfessor in GeometryUniversity of Palermo, ItalyPersonal Web-page 'This book provides a self-contained and well-organized introduction to a variety of fundamental concepts of Algebraic Geometry. It further helps readers to access Algebraic Geometry with minimal prerequisites. Thus, I highly recommend it as a textbook for Algebraic Geometry in undergraduate courses.' - Seonja KimProfessor in GeometryChungwoon University, Incheon, Republic of KoreaResearchgate Web-page (in English)Personal Web-page (original web page in Korean) 'A thorough, but gentle introduction to classical Algebraic Geometry, with plenty of examples and solved exercises, as well as all the necessary background in Commutative Algebra.' - Andreas L KnutsenProfessor in MathematicsUniversity of Bergen, NorwayPersonal Web-Page 'The book is a beautiful introduction to Algebraic Geometry. The author starts by recalling basic facts in Commutative Algebra, which makes the book quite self contained. Moreover it contains several examples and exercises with solutions, that allows students to navigate the study of Algebraic Geometry effectively. This book will become a reference!' - Alessandra SartiProfesseur et Directrice adjointe scientifique de 'Institut national des sciences mathématiques et de leurs interactions'Université de Poitiers, FrancePersonal Web-Page