Complex projective K3 surface

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: 24.

Dimension of the local deformation space: 20.

Betti numbers: b₀ = 1, b₁ = 0, b₂ = 22, b₃ = 0, b₄ = 1.

Chern numbers

• ∫c₂ = 24

Cohomology lattices

• H²(X; ℤ)/tors, with the cup-product intersection form: U^3 + E8(-1)^2.

Notes

The Hodge series and the intersection lattice are constant for complex K3 surfaces (Huybrechts 2016). The listed local deformation dimension concerns complex K3 surfaces; the projective locus has dimension 19 within each polarized family (Huybrechts 2016).