Kum^2-type

Hodge diamond

The entries are h^p,q = dim_ℂ H^q(X, Ω^p_X). Row k has p + q = k, with p increasing from left to right.

Symmetry group: D4.

Numerical invariants

Euler characteristic: 108.

Dimension of the local deformation space: 5.

Betti numbers: b₀ = 1, b₁ = 0, b₂ = 7, b₃ = 8, b₄ = 108, b₅ = 8, b₆ = 7, b₇ = 0, b₈ = 1.

Chern numbers

• ∫c₂c₂ = 756
• ∫c₄ = 108

Cohomology lattices

• H²(X; ℤ)/tors, with the Beauville–Bogomolov–Fujiki form: U^3 + <-6>.

Notes

The Hodge series is the n = 2 case of the generalized Kummer formula (Göttsche and Soergel 1993). The lattice and numerical invariants agree with the Kum^2 entry of the hyperkähler catalogue (Hyperkaehler.info, n.d.).