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<p>We determine the Néron-Severi lattices of <i>K</i>3 hypersurfaces with large Picard number in toric three-folds derived from Fano polytopes. On each <i>K</i>3 surface, we introduce a particular elliptic fibration. In the proof of the main theorem, we show that the Néron-Severi lattice of each <i>K</i>3 surface is generated by a general fibre, sections and appropriately selected components of the singular fibres of our elliptic fibration. Our argument gives a certain proof of the Dolgachev conjecture for Fano polytopes, which is a conjecture on mirror symmetry for <i>K</i>3 surfaces.</p>

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Elliptic fibrations on toric K3 hypersurfaces and mirror symmetry derived from Fano polytopes

  • 期刊论文

  • 发表日期：

    2025年5月21日

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  • Tomonao Matsumura,
  • Atsuhira Nagano

摘要

We determine the Néron-Severi lattices of K3 hypersurfaces with large Picard number in toric three-folds derived from Fano polytopes. On each K3 surface, we introduce a particular elliptic fibration. In the proof of the main theorem, we show that the Néron-Severi lattice of each K3 surface is generated by a general fibre, sections and appropriately selected components of the singular fibres of our elliptic fibration. Our argument gives a certain proof of the Dolgachev conjecture for Fano polytopes, which is a conjecture on mirror symmetry for K3 surfaces.