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. Section 2, including pairs, canonical bunde formula and Hodge theoretic interpretation of moduli divisor. Boundedness notions. (Simone Diverio)

• 8th April. Section 3, abelian fibrations and fibrations of Picard type. Period mapping of abelian varieties and Zahrin's trick. (Giulio Codogni)

• 15th Aprile. Section 3, Period mapping of primitive symplectic varieties, Kuga--Satake construction. Proof of effective b-semiampleness for abelian and psv fibrations. (Kieran O'Grady)

• 22rd april. Section 4, Boundedness of the relative polarisation in the case of a fibration of Picard type with a rational section.

• 29th April. Birational boundedness of the base and proof of Theorem 4.18 

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)