Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update of the most recent developments. It offers a comprehensive introduction to this fascinating topic, that will certainly become an essential reference for anybody working in this field. Rationality problems have been of fundamental importance both in algebra and algebraic geometry. Historically, rationality problems have motivated significant developments, as for example the theory of abelian integrals, Riemann surfaces and the Abel-Jacobi map; This work is aimed at researchers and graduate students in algebraic geometry.This work is aimed at researchers and graduate students in algebraic geometry Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments. It offers a comprehensive introduction to this fascinating topic, and will certainly become an essential referenc
e for anybody working in the field. Rationality problems are of fundamental importance both in algebra and algebraic geometry. Historically, rationality problems motivated significant developments in the theory of abelian integrals, Riemann surfaces and the Abel-Jacobi map, among other areas, and they have strong links with modern notions such as moduli spaces, Hodge theory, algebraic cycles and derived categories. This text is aimed at researchers and graduate students in algebraic geometry.
Introduction.-Arnaud Beauville: The Lüroth problem.-Brendan Hassett: Cubic Fourfolds, K3 Surfaces, and Rationality Questions.- Alexander Kuznetsov: Derived categories view on rationality problems.- Alessandro Verra: Classical moduli spaces and Rationality.- Howard Nuer: Unirationality of Moduli Spaces of Special Cubic Fourfolds and K3 Surfaces.
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