Authors: Stephen Coughlan ¹; Taro Sano ²

• 1 Mathematisches Institut [Bayreuth]
• 2 Kobe University

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.