论文标题
拉格朗日多段及其复曲面的镜子
Lagrangian multi-sections and their toric equivariant mirror
论文作者
论文摘要
Syz的猜想表明，民间传说“拉格朗日多段是镜像塑形矢量束”。在本文中，我们证明了这种民间传说在矢量空间的cotangent捆绑包中的拉格朗日多区域，这是通过Fang-liu-treumann-Zaslow的作品完成复曲面品种的镜像。我们还介绍了拉格朗日实现问题，该问题询问是否可以使用热带拉格朗日多部分规定的渐近条件来构建一个毫无打扰的拉格朗日多部分。我们通过完整的二维风扇解决了热带拉格朗日多部门的实现问题，该二维风扇满足了所谓的$ n $生成条件，并使用$ n \ geq 3 $。作为一个应用程序，我们表明，射影平面上的每个等级2曲奇矢量捆绑包都与拉格朗日多节相镜。
The SYZ conjecture suggests a folklore that "Lagrangian multi-sections are mirror to holomorphic vector bundles". In this paper, we prove this folklore for Lagrangian multi-sections inside the cotangent bundle of a vector space, which are equivariantly mirror to complete toric varieties by the work of Fang-Liu-Treumann-Zaslow. We also introduce the Lagrangian realization problem, which asks whether one can construct an unobstructed Lagrangian multi-section with asymptotic conditions prescribed by a tropical Lagrangian multi-section. We solve the realization problem for tropical Lagrangian multi-sections over a complete 2-dimensional fan that satisfy the so-called $N$-generic condition with $N\geq 3$. As an application, we show that every rank 2 toric vector bundle on the projective plane is mirror to a Lagrangian multi-section.
