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Gorenstein Formats, Canonical and Calabi–Yau Threefolds

Brown, Gavin; Kasprzyk, Alexander; Zhu, Lei


Gavin Brown

Lei Zhu


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.


Brown, G., Kasprzyk, A., & Zhu, L. (2022). Gorenstein Formats, Canonical and Calabi–Yau Threefolds. Experimental Mathematics, 31(1), 146-164.

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
Keywords Gorenstein format; Key variety; Threefold; General type; Calabi-Yau; Fano; Canonical orbitfold
Public URL
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