The Geometry of Cubic Hypersurfaces

‘What a beautiful book. Several turning points in algebraic geometry have in their background a cubic hypersurface. This superb exposition, by one of the masters in the field, takes the reader, in a friendly manner, through the fascinating, and occasionally mysterious, properties of these geometrical objects, and through them offers a glimpse of the underlying Hodge theory, of the theory of periods, the theory of motives, and the theory of derived categories. Graduate students, researchers, and colleagues will all find this unified treatment of cubic hypersurfaces profoundly inspiring.’ Enrico Arbarello, Accademia Nazionale dei Lincei‘This is just a fantastic book for students and experts alike. The geometry of cubics is a wonderful mix of the classical and the modern; Huybrechts consolidates the diverse results into a coherent account for the first time. His famously lucid writing clearly conveys the beauty of the geometry of these varieties. The book describes a plethora of techniques culminating in new (and really surprising) viewpoints on the subject.’ Richard Thomas, Imperial College London‘This exceedingly well written monograph covers material ranging from the very beginning of algebraic geometry, the 27 lines on a cubic surface, to highly relevant topical issues. The book will be a most valuable companion to algebraic geometers from graduate students to active researchers.’ Klaus Hulek, Leibniz University Hannover

Daniel Huybrechts is Professor in the Mathematical Institute of the University of Bonn. He previously held positions at Université Denis Diderot Paris 7 and the University of Cologne. He has published five books, including ‘Lectures on K3 Surfaces’ (2016) and ‘Fourier-Mukai Transforms in Algebraic Geometry’ (2006).