2025/07/01 by Engel, Philip, Filipazzi, Stefano, Greer, François +2 · 2 citations
#14J27 14J32 14J42 (Primary) 14D06 14E30 14D07 14K05 (Secondary) #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2507.00973
We prove that irreducible Calabi-Yau varieties of a fixed dimension, admitting a fibration by abelian varieties or primitive symplectic varieties of a fixed analytic deformation class, are birationally bounded. We prove that there are only finitely many deformation classes of primitive symplectic varieties of a fixed dimension, admitting a Lagrangian fibration. We also show that fibered Calabi-Yau 3-folds are bounded. Conditional on the generalized abundance or hyperkähler SYZ conjecture, our results prove that there are only finitely many deformation classes of hyperkähler varieties, of a fixed dimension, with b2 ≥ 5.