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.