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 ORCID-iD1; 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.

https://doi.org/10.46298/epiga.2018.volume2.4055
Source: HAL:hal-01627067v2
Volume: Volume 2
Published on: December 21, 2018
Accepted 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]
Licence: Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
Funding:
    Source : OpenAIRE Graph
  • Topological, Algebraic, Differential Methods in Classification and Moduli Theory; Funder: European Commission; Code: 340258

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