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 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 -manifolds in differential topology and the -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.
Keywords
Cite
@article{arxiv.2101.11841,
title = {Diffeomorphism classes of the doubling Calabi-Yau threefolds with Picard number two},
author = {Naoto Yotsutani},
journal= {arXiv preprint arXiv:2101.11841},
year = {2023}
}
Comments
Published in Rendiconti del Circolo Matematico di Palermo Series 2, (2023). https://link.springer.com/article/10.1007/s12215-022-00856-2