Algebraic Curves and Surfaces: A History of Shapes

This book collects lecture notes from the school TiME2019, which covers the theory and applications of algebraic curves and surfaces, including classical methods and recent developments. It aims to serve as a guide for both young mathematicians and experienced researchers.

Format: Hardback
Length: 205 pages
Publication date: 05 May 2023
Publisher: Springer International Publishing AG

This comprehensive volume compiles the lecture notes from the school TiME2019 (Treasures in Mathematical Encounters). With a multifaceted objective, this book seeks to provide a comprehensive overview of the diverse realm of algebraic curves and surfaces, including their higher-dimensional counterparts. It delves into the historical development that paved the way for the theory of algebraic surfaces, highlighting the contributions of Castelnuovo and Enriques in the classification theorem of algebraic surfaces. Moreover, it explores the application of classical geometric techniques, introduced by Castelnuovo, to study linear systems of hypersurfaces. Additionally, the book showcases algebraic methods employed to derive implicit equations of parametrized algebraic curves and surfaces, encompassing a range of techniques from classical elimination theory to modern tools involving syzygy theory and Castelnuovo-Mumford regularity. Recognizing the extensive and illustrious history of this subject, this book acknowledges its limitations in comprehensively covering all aspects of theory and applications. Nonetheless, it serves as a valuable guide for both aspiring mathematicians seeking to approach the field from a classical and computationally oriented perspective and experienced researchers seeking to explore recent applications.

Weight: 534g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031241505
Edition number: 1st ed. 2023