Mirror Symmetry — Calabi-Yau

Mirror symmetry is a duality between pairs of Calabi-Yau manifolds M and its mirror W, swapping the Hodge numbers h^p,q(M) ↔ h^q,p(W). The key exchange is h^1,1(M) = h^2,1(W) and h^2,1(M) = h^1,1(W) — counting complex structure deformations vs. Kähler deformations. The quintic threefold (h^1,1=1, h^2,1=101) mirrors with h^1,1=101, h^2,1=1. Candelas et al. used mirror symmetry to compute 2875 rational curves of degree 1 on the quintic — matching Clemens' 1986 result — and predicted 609250 conics (degree 2), later verified by algebraic geometers. The visualization shows a 2D projection of a Calabi-Yau slice rotating in parameter space.