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. Nous...

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Bibliographic Details
Published in:	Épijournal de géométrie algébrique Vol. 2; no. Article no.15
Main Authors:	Coughlan, Stephen, Sano, Taro
Format:	Journal Article
Language:	English
Published:	EPIGA 21-12-2018 Association Epiga
Series:	Volume 2 (2018)
Subjects:	[ math.math-ag ] mathematics [math]/algebraic geometry [math.ag] affine cones Algebraic Geometry deformations fano 3-folds k3 surfaces Mathematics Fano 3-folds Affine cones Deformations K3 surfaces
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Summary:	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. Nous montrons que le cône affine sur une surface K3 primitivement polarisée générale de genre g est lissable si et seulement si g≤ 10 ou g = 12. Nous exhibons également plusieurs exemples de singularités affichant des comportements spécifiques, tels que des surfaces dont le cône affine est lissable alors même que le cône projectif ne l'est pas.
ISSN:	2491-6765 2491-6765
DOI:	10.46298/epiga.2018.volume2.4055