Complete Calabi-Yau metrics from smoothing Calabi-Yau complete intersections

TL;DR

This paper constructs complete Calabi-Yau metrics on non-compact manifolds obtained by smoothing Calabi-Yau cones, extending previous work and allowing for metrics with varying complex structures and isolated singularities.

Contribution

It introduces a new method to produce complete Calabi-Yau metrics on smoothings of Calabi-Yau cones, broadening the class of known examples.

Findings

Constructed Calabi-Yau metrics with tangent cone at infinity as fC imes V_0

Extended previous work by Sze9kelyhidi (2019)

Produced metrics with fibers of varying complex structures and isolated singularities

Abstract

We construct complete Calabi-Yau metrics on non-compact manifolds that are smoothings of an initial complete intersection $V_0$ that is a Calabi-Yau cone, extending the work of Sz\'ekelyhidi (2019). The constructed Calabi-Yau manifold has tangent cone at infinity given by $\mathbb{C} \times V_0$. This construction produces Calabi-Yau metrics with fibers having varying complex structures and possibly isolated singularities.