Diffeomorphism classes of the doubling Calabi-Yau threefolds with Picard number two

Abstract

Previously we constructed Calabi-Yau threefolds by a differential-geometric gluing method using Fano threefolds with their smooth anticanonical $K3$ divisors (New York J. Math. 20: 1-33, 2014). In this paper, we further consider the diffeomorphism classes of the resulting Calabi-Yau threefolds (which are called the doubling Calabi-Yau threefolds) starting from different pairs of Fano threefolds with Picard number one. Using the classifications of simply-connected $6$-manifolds in differential topology and the $\lambda$-invariant introduced by Lee (J. Math. Pures Appl. 141: 195-219, 2020), we prove that any two of the doubling Calabi-Yau threefolds with Picard number two are not diffeomorphic to each other when the underlying Fano threefolds are distinct families.

Published in Rendiconti del Circolo Matematico di Palermo Series 2, (2023). https://link.springer.com/article/10.1007/s12215-022-00856-2

References in corpus (1)

• Mirror pairs of Calabi-Yau threefolds from mirror pairs of quasi-Fano threefolds