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 (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.

Published version in Geometriae Dedicata

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