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.

Source : oai:HAL:hal-01627067v2

Volume: Volume 2

Published on: December 21, 2018

Submitted on: November 7, 2017

Keywords: Fano 3-folds,K3 surfaces,Affine cones,Deformations,
[
MATH.MATH-AG
]
Mathematics [math]/Algebraic Geometry [math.AG]

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