Four-dimensional projective orbifold hypersurfaces
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 ari...
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| Format: | Article |
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Taylor & Francis
2015
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| Online Access: | https://eprints.nottingham.ac.uk/31032/ |
| _version_ | 1848794113442316288 |
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| author | Brown, Gavin Kasprzyk, Alexander M. |
| author_facet | Brown, Gavin Kasprzyk, Alexander M. |
| author_sort | Brown, Gavin |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:11:02Z |
| format | Article |
| id | nottingham-31032 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:11:02Z |
| publishDate | 2015 |
| publisher | Taylor & Francis |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-310322020-05-04T17:27:29Z https://eprints.nottingham.ac.uk/31032/ Four-dimensional projective orbifold hypersurfaces Brown, Gavin Kasprzyk, Alexander M. 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. Taylor & Francis 2015-12-08 Article PeerReviewed Brown, Gavin and Kasprzyk, Alexander M. (2015) Four-dimensional projective orbifold hypersurfaces. Experimental Mathematics, 25 (2). pp. 176-193. ISSN 1944-950X Fano Calabi-Yau Threefold Fourfold Orbifold Weighted Hypersurface http://www.tandfonline.com/doi/full/10.1080/10586458.2015.1054054 doi:10.1080/10586458.2015.1054054 doi:10.1080/10586458.2015.1054054 |
| spellingShingle | Fano Calabi-Yau Threefold Fourfold Orbifold Weighted Hypersurface Brown, Gavin Kasprzyk, Alexander M. Four-dimensional projective orbifold hypersurfaces |
| title | Four-dimensional projective orbifold hypersurfaces |
| title_full | Four-dimensional projective orbifold hypersurfaces |
| title_fullStr | Four-dimensional projective orbifold hypersurfaces |
| title_full_unstemmed | Four-dimensional projective orbifold hypersurfaces |
| title_short | Four-dimensional projective orbifold hypersurfaces |
| title_sort | four-dimensional projective orbifold hypersurfaces |
| topic | Fano Calabi-Yau Threefold Fourfold Orbifold Weighted Hypersurface |
| url | https://eprints.nottingham.ac.uk/31032/ https://eprints.nottingham.ac.uk/31032/ https://eprints.nottingham.ac.uk/31032/ |