Geodesic
Smoothing cones over K3 surfaces
Épijournal de Géométrie Algébrique, Tome 2 (2018)

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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. 
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     author = {Coughlan, Stephen and Sano, Taro},
     title = {Smoothing cones over {K3} surfaces},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
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     year = {2018},
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}
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Coughlan, Stephen; Sano, Taro. Smoothing cones over K3 surfaces. Épijournal de Géométrie Algébrique, Tome 2 (2018). doi: 10.46298/epiga.2018.volume2.4055

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