TL;DR
This paper provides an overview of the Lüroth problem, its historical context, counterexamples, and recent advances in stable rationality using new methods introduced by C. Voisin.
Contribution
It summarizes the development of the Lüroth problem, highlighting recent progress in stable rationality through innovative techniques.
Findings
Counterexamples to Lüroth problem from the 1970s
Recent methods by C. Voisin advancing stable rationality
Historical overview of the Lüroth problem
Abstract
Notes of my lectures at the CIME (Levico Terme, june 2015). The lectures gave an overview of the L\"uroth problem, its history, the counter-examples found in the 70's, and the recent developments on stable rationality following the new method introduced by C. Voisin.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Algebraic and Geometric Analysis · advanced mathematical theories