An Invitation to Modern Enumerative Geometry

This book provides a gentle introduction to enumerative geometry, focusing on counting invariants in algebraic geometry, with concrete calculations and proofs of background results. It is suitable for PhD students or research beginners in the field.

Format: Hardback
Length: 302 pages
Publication date: 15 December 2022
Publisher: Springer International Publishing AG

This captivating book is a testament to the author's profound insights and expertise in the field of enumerative geometry. It is a comprehensive resource that offers a gentle introduction to this rapidly evolving discipline, particularly focusing on the captivating realm of counting invariants in algebraic geometry. Beyond showcasing advanced techniques and providing meticulous explanations, this book goes the extra mile by presenting the proofs of numerous foundational results, ensuring a solid foundation for the theory.

Designed with graduate students and early-career researchers in mind, this text serves as a valuable entry point into the world of enumerative geometry. It provides a clear and concise roadmap for those seeking to delve into this captivating field. Whether you are a seasoned mathematician or a newcomer to the subject, this book offers a seamless and accessible journey through the complexities of enumerative geometry.

One of the remarkable features of this book is its versatility. It can be approached as an introduction to Hilbert schemes and Quot schemes on three-folds, offering a comprehensive overview of these important concepts. Moreover, it serves as an excellent primer on localisation formulae in enumerative geometry, providing a solid foundation for further exploration.

What sets this book apart is its accessibility without requiring a deep understanding of algebraic geometry. While it assumes a basic familiarity with the subject, three appendices—one on deformation theory, one on intersection theory, and one on virtual fundamental classes—are included to assist readers in diving deeper into the main material and enhancing their comprehension. These appendices serve as valuable resources, offering additional insights and tools to enrich the reader's journey.

In summary, this book is a must-read for anyone with an interest in enumerative geometry and its captivating applications. It provides a comprehensive and accessible introduction to the field, while also offering valuable insights and background information. With its clear writing style, meticulous proofs, and comprehensive appendices, this book is an invaluable resource for both students and researchers alike.

Weight: 647g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031114984
Edition number: 1st ed. 2022