Ebene algebraische Kurven

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In a comprehensive introduction to the theory of plane algebraic curves, the authors explore this classical area of mathematics, which has roots in ancient Greek studies and continues to inspire research today. Originating from course notes at the University of Bonn, the text emphasizes motivation, imagination, and understanding for students. Curves, as classical objects, are examined from various perspectives, providing a foundation for modern explorations of singularities. The first chapter features many special curves with appealing geometric presentations, complemented by a wealth of illustrations. It also introduces projective geometry over the complex numbers. The second chapter presents a straightforward proof of Bezout’s theorem alongside an in-depth discussion of cubics. Central to the text is the chapter on the resolution of singularities, focusing on complex numbers. Notably, the book offers insights into further research on the topics covered, with numerous references to the literature. A variety of examples enriches this successful representation of a classical yet vibrant subject.