Parameterized family

Kum^n-type

Parameter n ≥ 2.

Instances

Notes

For an abelian surface A, the generalized Kummer variety is the fiber over zero of the sum map from A1 to A. Its complex dimension is 2n (Beauville 1983). The Hodge series is given by Göttsche and Soergel (Göttsche and Soergel 1993). The hyperkähler catalogue lists individual values (Hyperkaehler.info, n.d.).

Beauville, Arnaud. 1983. “Variétés kählériennes Dont La Première Classe de Chern Est Nulle.” Journal of Differential Geometry 18 (4): 755–82. https://doi.org/10.4310/jdg/1214438181.
Göttsche, Lothar, and Wolfgang Soergel. 1993. “Perverse Sheaves and the Cohomology of Hilbert Schemes of Smooth Algebraic Surfaces.” Mathematische Annalen 296 (2): 235–45. https://doi.org/10.1007/BF01445104.
Hyperkaehler.info: The Geography of Compact Irreducible Holomorphic Symplectic Varieties. n.d. https://hyperkaehler.info/.

  1. n+1↩︎