By Fedor Bogomolov,Yuri Tschinkel
Rationality difficulties hyperlink algebra to geometry, and the problems concerned depend upon the transcendence measure of $K$ over $k$, or geometrically, at the measurement of the range. an incredible good fortune in nineteenth century algebraic geometry was once an entire resolution of the rationality challenge in dimensions one and over algebraically closed flooring fields of attribute 0. Such advances has ended in many interdisciplinary functions to algebraic geometry.
This finished booklet comprises surveys of analysis papers by means of prime experts within the box and offers symptoms for destiny study in rationality difficulties. issues mentioned contain the rationality of quotient areas, cohomological invariants of quasi-simple Lie sort 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 in particular 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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Cohomological and Geometric Approaches to Rationality Problems: New Perspectives: 282 (Progress in Mathematics) by Fedor Bogomolov,Yuri Tschinkel