Boundedness of fibred K-trivial varieties RG
In Spring 2026 we are organising a reading group on the boundedness of K-trivial varieties following the recent article Boundedness of some fibred $K$-trivial varieties .
We meet every week on Wednesday at 10:30 am in Aula L at the Dipartimento di Matematica G. Castelnuovo.
Dates:
4th March. Motivation and overview of the (first half of the) article (Fabio Bernasconi)
25th March. Fibrations of Picard type, statements of the main theorem and plan of the proof (Fabio Bernasconi) Canonical bundle formula for elliptic surface fibrations and log canonical thresholds. (Simone Diverio)
1st April: Period mapping of abelian varieties, Zahrin's trick and boundedness of fibration of Picard type. (Giulio Codogni)
8th April. Section 3, Canonical bundle formula (Simone Diverio)
15th Aprile. Proof of the results of the article in the case of elliptic K3 surfaces. Primitive symplectic varieties. (Kieran O'Grady)
22rd april. Section 4, Period mapping of primitive symplectic varieties, Kuga--Satake construction. (Kieran O'Grady)
29th April. Effective semi-ampleness for abelian fiberations and final overview (Fabio Bernasconi)
References:
P. Engel, S. Filipazzi, F. Greer, M. Mauri and R. Svaldi. Boundedness of some fibered K-trivial varieties.
J. Kollár. Kodaira's canonical bundle formula and adjunction, in Flips for 3-folds and 4-folds. (for a summary on the canonical bundle formula)
C. Peter, J.Steenbrink. Mixed Hodge Structures (for a summary on VHS, Schmid's extension and period domains).
B. Bakker, C. Lehn. The global moduli theory of symplectic varieties. J. Reine Angew. Math. 790 (2022), 223--265 (for the theory of singular holomorphic symplectic variety)
D. Huybrechts, Lectures on K3 surfaces. Cambridge Studies in Advanced Mathematics, 158. (for the Kuga--Satake construction)
C. Birkar, G. Di Cerbo and R. Svaldi. Boundedness of elliptic Calabi-Yau varieties with a rational section. (for the boundedness results on rationally connected klt CY pairs)