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Cohomological and Geometric Approaches to Rationality Problems (eBook, PDF)

New Perspectives

Redaktion: Bogomolov, Fedor; Tschinkel, Yuri
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Rationality problems link algebra to geometry, and the difficulties involved depend on the transcendence degree of $K$ over $k$, or geometrically, on the dimension of the variety. A major success in 19th century algebraic geometry was a complete solution of the rationality problem in dimensions one and two over algebraically closed ground fields of characteristic zero. Such advances has led to many interdisciplinary applications to algebraic geometry.This comprehensive book consists of surveys of research papers by leading specialists in the field and gives indications for future research in r...

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