Algebraic Geometry Explained

Pasquale De Marco

Summary

Embark on a captivating journey through the world of algebraic geometry with this comprehensive and accessible guide. Delve into the intricate relationship between algebra and geometry, uncovering the hidden structures that govern the behavior of geometric objects.

Discover the foundations of algebraic geometry, where we lay the groundwork for understanding algebraic varieties, the central objects of study in this field. Explore the concept of schemes, a generalized notion of space that extends the familiar concept of varieties, providing a powerful framework for studying geometric objects in great generality.

Unravel the mysteries of curves, the simplest and most fundamental type of algebraic variety. Investigate their properties, classifications, and applications, uncovering their significance in diverse fields such as cryptography and error-correcting codes.

Explore the realm of surfaces, two-dimensional varieties with rich geometric and topological structures. Discover quadrics, ruled and developable surfaces, and embark on a journey to classify these surfaces, revealing their unique characteristics and applications in architecture and engineering.

Venture into the vast landscape of higher-dimensional varieties, where we uncover the intricate interplay between geometry and topology. Investigate intersections and cohomology, unveiling the topological secrets of varieties. Delve into the concept of divisors and linear systems, gaining insights into the behavior of algebraic varieties.

Witness the power of algebraic geometry as we explore its diverse applications. Discover the connections between algebraic geometry and coding theory, cryptography, physics, and number theory, showcasing the remarkable versatility of this mathematical discipline.

With clear explanations, engaging examples, and insightful connections to other areas of mathematics, this book is an essential resource for students, researchers, and anyone fascinated by the beauty and power of algebraic geometry. Immerse yourself in the world of algebraic geometry and uncover the hidden elegance that lies at the intersection of algebra and geometry.

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Available since: 06/02/2025.

Print length: 163 pages.

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