| Résume | it is a question of great interest to construct meaningful compactifications for the moduli of algebraic varieties of a specified type. For varieties of general type, and Fano type a fairly complete understanding of the compactification problem was obtained recently via the KSBA theory and respectively K-theory. The remaining case, that of K-trivial varieties turns out to be particularly challenging and the same time very interesting. After reviewing what we know in this case (especially new results, due to Alexeev-Engel for K3 surfaces), I will propose a canonical minimal compactification for the K-trivial case and discuss some evidence towards it. (Versions of this conjecture previously occur in work of Ambro/Fujino/Shokurov, Odaka, and respectively GGLR)
The point of view taken here is that of Hodge theory.
The talk is based on some joint work with R. Friedman. It is also closely related to joint work with Kollár, Saccà, Voisin [KLSV18] and respectively Green, Griffiths, and Robles [GGLR20]. |
