标题： 拉格朗日纤维化在环面流形的爆破上的研究及超曲面的镜像对称性 显示英文标题

标题： Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces

摘要： 我们从 Strominger-Yau-Zaslow (SYZ) 猜想的角度考虑 (本质上任意的) 在 (可能非紧致的) toric 变量中的超曲面的镜像对称性。 给定一个 toric 变量$V$中的超曲面$H$，我们在正性假设下构造了一个 Landau-Ginzburg 模型，该模型是$V\times\mathbb{C}$沿$H\times 0$的爆破的 SYZ 镜像。 此构造还给出了仿射二次曲线丛的 SYZ 镜像，以及一个可以自然地视为$H$的镜像的 Landau-Ginzburg 模型。 主要应用涉及一般类型的仿射超曲面，我们的结果为近期文献中出现的各种镜像对称陈述提供了几何基础。 我们还得到了关于完备交集的类似结果。 显示英文摘要

摘要： We consider mirror symmetry for (essentially arbitrary) hypersurfaces in (possibly noncompact) toric varieties from the perspective of the Strominger-Yau-Zaslow (SYZ) conjecture. Given a hypersurface $H$ in a toric variety $V$ we construct a Landau-Ginzburg model which is SYZ mirror to the blowup of $V\times\mathbb{C}$ along $H\times 0$, under a positivity assumption. This construction also yields SYZ mirrors to affine conic bundles, as well as a Landau-Ginzburg model which can be naturally viewed as a mirror to $H$. The main applications concern affine hypersurfaces of general type, for which our results provide a geometric basis for various mirror symmetry statements that appear in the recent literature. We also obtain analogous results for complete intersections.