Numerical Weil-Petersson metrics on moduli spaces of Calabi-Yau manifolds

Understand

We introduce a simple and very fast algorithm that computes Weil-Petersson metrics on moduli spaces of polarized Calabi-Yau manifolds.

• Also, by using Donaldson's quantization link between the infinite and finite dimensional G.I.T quotients that describe moduli spaces of varieties, we define a natural sequence of Kaehler metrics.
• We prove that the sequence converges to the Weil-Petersson metric.
• We also develop an algorithm that numerically approximates such metrics, and hence the Weil-Petersson metric itself.