Conifold Transitions for Complete Intersection Calabi-Yau 3-folds in Products of Projective Spaces

TL;DR

This paper demonstrates that generic complete intersection Calabi-Yau 3-folds in products of projective spaces can undergo conifold transitions to connected sums of S^3 × S^3, revealing new complex structures with trivial canonical bundles.

Contribution

It extends conifold transition techniques to Calabi-Yau 3-folds in products of projective spaces, generalizing previous work on quintic threefolds.

Findings

Existence of conifold transitions for these Calabi-Yau 3-folds.

Construction of complex structures with trivial canonical bundles on connected sums of S^3 × S^3.

New examples of Calabi-Yau manifolds via conifold transitions.

Abstract

We prove that a generic complete intersection Calabi-Yau 3-fold defined by sections of ample line bundles on a product of projective spaces admits a conifold transition to a connected sum of S^{3} \times S^{3}. In this manner, we obtain complex structures with trivial canonical bundles on some connected sums of S^{3} \times S^{3}. This construction is an analogue of that made by Friedman, Lu and Tian who used quintics in P^{4}.