The present paper is dedicated to illustrating an extension of polar duality between Fano toric varieties to a more general duality, called framed duality, so giving rise to a powerful and unified method of producing mirror partners of hypersurfaces and complete intersections in toric varieties, of any Kodaira dimension. In particular, the class of projective hypersurfaces and their mirror partners are studied in detail. Moreover, many connections with known Landau–Ginzburg mirror models, Homological Mirror Symmetry and Intrinsic Mirror Symmetry, are discussed.

中文翻译：

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复曲面品种的极性二元性的扩展及其在镜像对称性中的后果

本论文致力于说明 Fano 复曲面簇之间的极性对偶性扩展到更一般的对偶性，称为框架对偶性，因此产生了一种强大而统一的方法来产生超曲面的镜像伙伴和复曲面簇的完全交集，任何小平次元。特别是，详细研究了射影超曲面的类别及其镜像伙伴。此外，还讨论了与已知的 Landau-Ginzburg 镜像模型、同源镜像对称和固有镜像对称的许多联系。