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- W4289785191 abstract "We determine the N'eron-Severi lattices of $K3$ hypersurfaces with large Picard number in toric three-folds derived from Fano polytopes. Such $K3$ surfaces are important objects of research in mirror symmetry. On each $K3$ surface, we introduce a particular elliptic fibration which induces a Mordell-Weil group of rank $1$. In the proof of the main theorem, we show that the N'eron-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 down-to-earth proof of the Dolgachev conjecture for Fano polytopes, which is a conjecture on mirror symmetry for $K3$ surfaces." @default.
- W4289785191 created "2022-08-04" @default.
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- W4289785191 date "2022-08-02" @default.
- W4289785191 modified "2023-09-29" @default.
- W4289785191 title "Elliptic fibrations on toric $K3$ hypersurfaces and mirror symmetry derived from Fano polytopes" @default.
- W4289785191 doi "https://doi.org/10.48550/arxiv.2208.01465" @default.
- W4289785191 hasPublicationYear "2022" @default.
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