Numerical Calabi-Yau metrics

TL;DR

This paper introduces numerical techniques to approximate Ricci-flat metrics on Calabi-Yau hypersurfaces, leveraging balanced metrics and building on Donaldson's theoretical framework, with detailed examples and potential extensions.

Contribution

It presents a novel numerical approach for Calabi-Yau metrics using balanced metrics, expanding computational tools in complex geometry.

Findings

Successful approximation of Ricci-flat metrics on Calabi-Yau hypersurfaces

Application to a family of quintic threefolds demonstrating method effectiveness

Proposals for extending the numerical methods to broader classes

Abstract

We develop numerical methods for approximating Ricci flat metrics on Calabi-Yau hypersurfaces in projective spaces. Our approach is based on finding balanced metrics, and builds on recent theoretical work by Donaldson. We illustrate our methods in detail for a one parameter family of quintics. We also suggest several ways to extend our results.