Gorenstein Formats, Canonical and Calabi–Yau Threefolds

Brown, Gavin; Kasprzyk, Alexander; Zhu, Lei

Abstract

Gorenstein formats present the equations of regular canonical, Calabi–Yau and Fano varieties embedded by subcanonical divisors. We present a new algorithm for the enumeration of these formats based on orbifold Riemann-Roch and knapsack packing-type algorithms. We apply this to extend the known lists of threefolds of general type beyond the well-known classes of complete intersections and also to find classes of Calabi-Yau threefolds with canonical singularities.

Citation

Brown, G., Kasprzyk, A., & Zhu, L. (2022). Gorenstein Formats, Canonical and Calabi–Yau Threefolds. Experimental Mathematics, 31(1), 146-164. https://doi.org/10.1080/10586458.2019.1592036

• Journal Article Type: Article
• Acceptance Date: Jan 20, 2019
• Online Publication Date: Apr 23, 2019
• Publication Date: 2022
• Deposit Date: Mar 14, 2019
• Publicly Available Date: Apr 26, 2019
• Journal: Experimental Mathematics
• Print ISSN: 1058-6458
• Electronic ISSN: 1944-950X
• Publisher: Taylor & Francis Open
• Peer Reviewed: Peer Reviewed
• Volume: 31
• Issue: 1
• Pages: 146-164
• DOI: https://doi.org/10.1080/10586458.2019.1592036
• Keywords: Gorenstein format; Key variety; Threefold; General type; Calabi-Yau; Fano; Canonical orbitfold
• Public URL: https://nottingham-repository.worktribe.com/output/1605893
• Publisher URL: https://www.tandfonline.com/doi/full/10.1080/10586458.2019.1592036