ERC Starting Grant · 2020
Rationality of varieties and algebraic cycles
This proposal uses algebraic cycles and unramified cohomology to attack fundamental questions about the rationality, stable rationality and unirationality of rationally connected varieties, the integral Hodge conjecture for abelian varieties, as well as the Griffiths-Harris conjecture about curves on three-dimensional hypersurfaces. A breakthrough of Voisin, with improvements by Colliot-Thélène--Pirutka and myself (Duke Math. J. 2019), recently led to tremendous advances in our understanding of (stable) rationality of rationally connected varieties. For instance, this allowed me (Journal of the AMS 2019) to solve the rationality problem for hypersurfaces under a logarithmic degree bound,…
From the public funding record at EU CORDIS. Describes the funded project, not the reviews below.