Algebraic Curves and Surfaces

Laurent Busé received his PhD degree in Mathematics at the Université of Nice - Sophia Antipolis in 2001 and he is currently a senior researcher at the Inria research center of Université Côte d’Azur. His main research interests focus on computational methods in algebraic geometry and commutative algebra, more specifically on elimination theory, the geometry of algebraic curves and surfaces and their applications in the fields of geometric modeling and geometry processing.Fabrizio Catanese studied at the Universita’ di Pisa and Scuola Normale Superiore 1968-1974, held the Chair of Geometry 1980-1997 in Pisa, the Gauss Chair of Complex Analysis in Goettingen, 1997-2001, then has been professor in Bayreuth since 2001. He is Research Scholar at the Korean Institute for Advanced Study and member of the Accademia Nazionale dei Lincei, the Goettingen Academy, the Academia Europaea. He has been visiting professor at many international Universities and research centres. Elisa Postinghel received her PhD in Mathematics from the University Roma Tre in 2010. She was a lecturer at Loughborough University between 2016 and 2020 and she is currently a senior researcher at the University of Trento. Her research work is in algebraic geometry; her main interests span classical topics such as polynomial interpolation problems on higher dimensional varieties as well as birational geometry and positivity properties of divisors and curves on Mori dream spaces.

“The geometry of algebraic curves and surfaces is a wide and venerable subject, and there are many monographs and textbooks aimed to graduate students and experienced researchers. … The book can be used as a gentle introduction to the theory of algebraic surfaces in conjunction with more systematic textbooks such as C. Ciliberto’s Classification of Complex Algebraic Surfaces.” (Felipe Zaldivar, MAA Reviews, July 30, 2023)

• - The P12-Theorem: The Classification of Surfaces and Its Historical Development. - Linear Systems of Hypersurfaces with Singularities and Beyond. - Implicit Representations of Rational Curves and Surfaces.