Stephen Coughlan ; Taro Sano - Smoothing cones over K3 surfaces

epiga:4055 - Épijournal de Géométrie Algébrique, December 21, 2018, Volume 2 - https://doi.org/10.46298/epiga.2018.volume2.4055
Smoothing cones over K3 surfaces

Authors: Stephen Coughlan ; Taro Sano

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.


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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