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<p>We take a first step towards the classification of singular Mori dream <i>K</i>3 surfaces. We prove that if the Picard lattice of a singular <i>K</i>3 surface is Mori dream, then the surface is Mori dream. Moreover, we show that for singular <i>K</i>3 surfaces, of Picard rank two, being Mori dream is equivalent to contain two negative curves intersecting each other, and apply this result to study Mori dreamness of <i>K</i>3 surfaces with a singular point of type <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="209_2025_3769_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(A_n\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>A</mi> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation>.</p>

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Mori dream singular K3 surfaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月16日

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  • Antonio Laface,
  • Alex Massarenti,
  • William D. Montoya

摘要

We take a first step towards the classification of singular Mori dream K3 surfaces. We prove that if the Picard lattice of a singular K3 surface is Mori dream, then the surface is Mori dream. Moreover, we show that for singular K3 surfaces, of Picard rank two, being Mori dream is equivalent to contain two negative curves intersecting each other, and apply this result to study Mori dreamness of K3 surfaces with a singular point of type \(A_n\) A n .