Four-dimensional projective orbifold hypersurfaces

Brown, Gavin; Kasprzyk, Alexander M.

Abstract

We classify four-dimensional quasismooth weighted hypersurfaces with small canonical class, and verify a conjecture of Johnson and Kollar on infinite series of quasismooth hypersurfaces with anticanonical hyperplane section in the case of fourfolds. By considering the quotient singularities that arise, we classify those weighted hypersurfaces that are canonical, Calabi-Yau, and Fano fourfolds. We also consider other classes of hypersurfaces, including Fano hypersurfaces of index greater than 1 in dimensions 3 and 4.

Citation

Brown, G., & Kasprzyk, A. M. (2015). Four-dimensional projective orbifold hypersurfaces. Experimental Mathematics, 25(2), https://doi.org/10.1080/10586458.2015.1054054

• Journal Article Type: Article
• Publication Date: Dec 8, 2015
• Deposit Date: Dec 10, 2015
• Publicly Available Date: Dec 10, 2015
• Journal: Experimental Mathematics
• Print ISSN: 1058-6458
• Electronic ISSN: 1944-950X
• Publisher: Taylor & Francis Open
• Peer Reviewed: Peer Reviewed
• Volume: 25
• Issue: 2
• DOI: https://doi.org/10.1080/10586458.2015.1054054
• Keywords: Fano, Calabi-Yau, Threefold, Fourfold, Orbifold, Weighted Hypersurface
• Public URL: https://nottingham-repository.worktribe.com/output/769741
• Publisher URL: http://www.tandfonline.com/doi/full/10.1080/10586458.2015.1054054
• Related Public URLs: http://www.tandfonline.com/loi/uexm20
• Additional Information: This is an Accepted Manuscript of an article published by Taylor & Francis in Experimental Mathematics on 08/12/2015 available online: http://www.tandfonline.com/doi/full/10.1080/10586458.2015.1054054