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

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 Székelyhidi (Duke Math J 168(14):2651–2700, 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.