By Fedor Bogomolov,Brendan Hassett,Yuri Tschinkel

This publication good points contemporary advancements in a swiftly growing to be sector on the interface of higher-dimensional birational geometry and mathematics geometry. It makes a speciality of the geometry of areas of rational curves, with an emphasis on purposes to mathematics questions. Classically, mathematics is the examine of rational or fundamental strategies of diophantine equations and geometry is the examine of traces and conics. From the trendy point of view, mathematics is the learn of rational and indispensable issues on algebraic types over nonclosed fields. an incredible perception of the twentieth century was once that mathematics houses of an algebraic kind are tightly associated with the geometry of rational curves at the type and the way they range in families.

This number of solicited survey and study papers is meant to function an advent for graduate scholars and researchers drawn to getting into the sphere, and as a resource of reference for specialists engaged on comparable difficulties. themes that might be addressed comprise: birational houses equivalent to rationality, unirationality, and rational connectedness, lifestyles of rational curves in prescribed homology sessions, cones of rational curves on rationally hooked up and Calabi-Yau kinds, in addition to comparable questions in the framework of the minimum version Program.

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