Smoothing cones over K3 surfaces
We prove that the affine cone over a general primitively polarised K3 surface of genus g is smoothable if and only if g ≤ 10 or g = 12. We also give several examples of singularities with special behaviour, such as surfaces whose affine cone is smoothable even though the projective cone is not.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Association Epiga
2018-12-01
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| Series: | Épijournal de Géométrie Algébrique |
| Subjects: | |
| Online Access: | https://epiga.episciences.org/4055/pdf |
| _version_ | 1811340828707127296 |
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| author | Stephen Coughlan Taro Sano |
| author_facet | Stephen Coughlan Taro Sano |
| author_sort | Stephen Coughlan |
| collection | DOAJ |
| description | We prove that the affine cone over a general primitively polarised K3 surface of genus g is smoothable if and only if g ≤ 10 or g = 12. We also give several examples of singularities with special behaviour, such as surfaces whose affine cone is smoothable even though the projective cone is not. |
| first_indexed | 2024-04-13T18:47:41Z |
| format | Article |
| id | doaj.art-ee1949ba61f741d1a946738545725efe |
| institution | Directory Open Access Journal |
| issn | 2491-6765 |
| language | English |
| last_indexed | 2024-04-13T18:47:41Z |
| publishDate | 2018-12-01 |
| publisher | Association Epiga |
| record_format | Article |
| series | Épijournal de Géométrie Algébrique |
| spelling | doaj.art-ee1949ba61f741d1a946738545725efe2022-12-22T02:34:33ZengAssociation EpigaÉpijournal de Géométrie Algébrique2491-67652018-12-01Volume 210.46298/epiga.2018.volume2.40554055Smoothing cones over K3 surfacesStephen Coughlanhttps://orcid.org/0000-0001-7817-1748Taro SanoWe prove that the affine cone over a general primitively polarised K3 surface of genus g is smoothable if and only if g ≤ 10 or g = 12. We also give several examples of singularities with special behaviour, such as surfaces whose affine cone is smoothable even though the projective cone is not.https://epiga.episciences.org/4055/pdffano 3-foldsk3 surfacesaffine conesdeformations[ math.math-ag ] mathematics [math]/algebraic geometry [math.ag] |
| spellingShingle | Stephen Coughlan Taro Sano Smoothing cones over K3 surfaces Épijournal de Géométrie Algébrique fano 3-folds k3 surfaces affine cones deformations [ math.math-ag ] mathematics [math]/algebraic geometry [math.ag] |
| title | Smoothing cones over K3 surfaces |
| title_full | Smoothing cones over K3 surfaces |
| title_fullStr | Smoothing cones over K3 surfaces |
| title_full_unstemmed | Smoothing cones over K3 surfaces |
| title_short | Smoothing cones over K3 surfaces |
| title_sort | smoothing cones over k3 surfaces |
| topic | fano 3-folds k3 surfaces affine cones deformations [ math.math-ag ] mathematics [math]/algebraic geometry [math.ag] |
| url | https://epiga.episciences.org/4055/pdf |
| work_keys_str_mv | AT stephencoughlan smoothingconesoverk3surfaces AT tarosano smoothingconesoverk3surfaces |