By Fedor Bogomolov,Yuri Tschinkel
Rationality difficulties hyperlink algebra to geometry, and the problems concerned rely on the transcendence measure of $K$ over $k$, or geometrically, at the measurement of the range. an immense luck in nineteenth century algebraic geometry used to be a whole resolution of the rationality challenge in dimensions one and over algebraically closed flooring fields of attribute 0. Such advances has resulted in many interdisciplinary functions to algebraic geometry.
This complete e-book includes surveys of analysis papers via prime experts within the box and offers symptoms for destiny learn in rationality difficulties. subject matters mentioned contain the rationality of quotient areas, cohomological invariants of quasi-simple Lie style teams, rationality of the moduli area of curves, and rational issues on algebraic varieties.
This quantity is meant for researchers, mathematicians, and graduate scholars drawn to algebraic geometry, and particularly in rationality problems.
Contributors: F. Bogomolov; T. Petrov; Y. Tschinkel; Ch. Böhning; G. Catanese; I. Cheltsov; J. Park; N. Hoffmann; S. J. Hu; M. C. Kang; L. Katzarkov; Y. Prokhorov; A. Pukhlikov
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