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.

Flamini, F. (2023). A first course in Algebraic Geometry and Algebraic Varieties. London : World Scientific Publishing (UK) Ltd. [10.1142/q0373].

A first course in Algebraic Geometry and Algebraic Varieties

Flamini F
Conceptualization
2023-03-01

Abstract

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.
1-mar-2023
Settore MAT/03 - GEOMETRIA
English
Rilevanza internazionale
Monografia
Algebraic Geometry
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.
https://www.worldscientific.com/worldscibooks/10.1142/q0373#t=aboutBook
Flamini, F. (2023). A first course in Algebraic Geometry and Algebraic Varieties. London : World Scientific Publishing (UK) Ltd. [10.1142/q0373].
Monografia
Flamini, F
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/321760
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