Number of triple points on complete intersection Calabi–Yau threefolds
Volume 131 / 2023
Annales Polonici Mathematici 131 (2023), 141-151
MSC: Primary 14J17; Secondary 14J32, 14J30.
DOI: 10.4064/ap230213-20-8
Published online: 10 October 2023
Abstract
We discuss bounds for the number of ordinary triple points on complete intersection Calabi–Yau threefolds in projective spaces and for Calabi–Yau threefolds in weighted projective spaces. In particular, we show that in $\mathbb {P}^5$ the intersection of a quadric and a quartic cannot have more than ten ordinary triple points. We provide examples of complete intersection Calabi–Yau threefolds with multiple triple points. We obtain the exact bound for a sextic hypersurface in $\mathbb {P}[1:1:1:1:2]$, which is $10$. We also discuss Calabi–Yau threefolds that cannot admit triple points.
