CONIFOLD TRANSITIONS FOR COMPLETE INTERSECTION CALABI–YAU THREEFOLDS IN PRODUCTS OF PROJECTIVE SPACES

We prove that a generic complete intersection Calabi–Yau threefold defined by sections of ample line bundles on a product of projective spaces admits a conifold transition to a connected sum of S3 × S3. In this manner, we obtain complex structures with trivial canonical bundles on some connected sums of S3 × S3. This construction is an analogue of that made by Friedman, Lu and Tian who used quintics in ℙ4.