Smoothing cones over K3 surfaces

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 discuss connections with the classification of Fano threefolds, and several examples of singularities with special behaviour.

Domaines: Géométrie algébrique [math.AG]

Stephen Coughlan, Taro Sano. Smoothing cones over K3 surfaces. 2017. ⟨hal-01627067v1⟩