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

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}.