Calabi-Yau Metrics for Quotients and Complete Intersections

TL;DR

This paper extends the computation of Calabi-Yau metrics to more complex geometries including quotients and complete intersections, providing new numerical insights into their dependence on various moduli.

Contribution

It introduces methods for calculating Calabi-Yau metrics on a broader class of manifolds, including quotients and complete intersections, with detailed numerical analysis.

Findings

Successful construction of metrics on generic quintics and quotients

Numerical analysis of Donaldson's algorithm dependence

Insights into metric behavior under moduli variations

Abstract

We extend previous computations of Calabi-Yau metrics on projective hypersurfaces to free quotients, complete intersections, and free quotients of complete intersections. In particular, we construct these metrics on generic quintics, four-generation quotients of the quintic, Schoen Calabi-Yau complete intersections and the quotient of a Schoen manifold with Z_3 x Z_3 fundamental group that was previously used to construct a heterotic standard model. Various numerical investigations into the dependence of Donaldson's algorithm on the integration scheme, as well as on the Kahler and complex structure moduli, are also performed.