Séminaire de Géométrie Complexe
Recent advances in the moduli theory of Calabi–Yau varieties
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Europe/Paris
Description
Conjecturally, any algebraic variety should admit a decomposition into varieties with positive, negative, or trivial canonical bundle. While the moduli theory of varieties with positive or negative canonical bundle is by now well-established, the case of Calabi–Yau varieties remains quite elusive. Key open problems include understanding how many moduli spaces of Calabi–Yau varieties exist in each fixed dimension, and whether there exist functorial compactifications of these moduli spaces. In this talk, I will survey some recent progress in this direction, obtained in collaboration with Engel, Filipazzi, Greer, Svaldi, and with Bakker, Filipazzi, and Tsimerman.