Topics in Algebraic Geometry (Rationality Problems)

Rational, stably rational, unirational, and rationally connected varieties. Rationality for quadric hypersurfaces and cubic surfaces. Castelnuovo criterion. Kollár’s reduction argument. Clemens-Griffiths obstruction. Artin-Mumford example. Noether-Fano method. Other possible topics include the decomposition of the diagonal, universal CH_0-triviality, and rationality in families.

References:
KOLLÁR J., SMITH K. E., CORTI A. – Rational and nearly rational varieties, Cambridge Studies in Math., 2004.
BEAUVILLE A., HASSETT B., KUZNETSOV A., VERRA A. – Rationality problems in algebraic geometry, Springer, 2016.
HOCHENEGGER A., LEHN M., STELLARI P. – Birational geometry of hypersurfaces, Springer, 2018.
KOLLÁR J. – Rational curves on algebraic varieties, Springer, 1996.