By Fedor Bogomolov,Brendan Hassett,Yuri Tschinkel
This ebook positive aspects contemporary advancements in a speedily growing to be zone on the interface of higher-dimensional birational geometry and mathematics geometry. It specializes in the geometry of areas of rational curves, with an emphasis on purposes to mathematics questions. Classically, mathematics is the research of rational or essential ideas of diophantine equations and geometry is the learn of strains and conics. From the trendy point of view, mathematics is the learn of rational and vital issues on algebraic forms over nonclosed fields. an important perception of the 20 th century was once that mathematics houses of an algebraic style are tightly associated with the geometry of rational curves at the kind and the way they range in families.
This choice of solicited survey and examine papers is meant to function an creation for graduate scholars and researchers attracted to coming into the sector, and as a resource of reference for specialists engaged on comparable difficulties. subject matters that may be addressed comprise: birational houses akin to rationality, unirationality, and rational connectedness, lifestyles of rational curves in prescribed homology periods, cones of rational curves on rationally hooked up and Calabi-Yau forms, in addition to comparable questions in the framework of the minimum version Program.
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Birational Geometry, Rational Curves, and Arithmetic (Simons Symposia) by Fedor Bogomolov,Brendan Hassett,Yuri Tschinkel