Numerical Weil-petersson Metrics on Moduli Spaces of Calabi-yau Manifolds
نویسندگان
چکیده
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 Kähler 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. Explicit examples are provided on a family of Calabi-Yau Quintic hypersurfaces in CP. The scope of our second algorithm is much broader; the same techniques can be used to approximate metrics on null spaces of Dirac operators coupled to Hermite Yang-Mills connections.
منابع مشابه
Weil-petersson Geometry on Moduli Space of Polarized Calabi-yau Manifolds
Moduli spaces of general polarized algebraic varieties are studied extensively by algebraic geometers. However, there are two classes of moduli spaces where the methods of differential geometry are equally powerful. These are the moduli spaces of curves and the moduli spaces of polarized Calabi-Yau manifolds. Both spaces are complex orbifolds. The Weil-Petersson metric is the main tool for inve...
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