We describe a notion of lattice polarization for rational elliptic surfaces and weak del Pezzo surfaces, and describe the complex moduli of the former and the Kahler cone of the latter. We then propose a version of mirror symmetry relating these two objects, which should be thought of as a form of Fano-LG correspondence. Finally, we relate this notion to other forms of mirror symmetry, including Dolgachev-Nikulin-Pinkham mirror symmetry for lattice polarized K3 surfaces and the Gross-Siebert program.

中文翻译：

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晶格极化 del Pezzo 表面的镜面对称

我们描述了有理椭圆表面和弱德尔佩佐表面的晶格极化概念，并描述了前者的复模量和后者的 Kahler 锥。然后，我们提出了一种与这两个对象相关的镜像对称版本，这应该被认为是 Fano-LG 对应的一种形式。最后，我们将这个概念与其他形式的镜像对称联系起来，包括用于晶格极化 K3 表面的 Dolgachev-Nikulin-Pinkham 镜像对称和 Gross-Siebert 程序。