论文标题
拉格朗日submanifolds的热带几何形状和无障碍的实现性
Realizability in tropical geometry and unobstructedness of Lagrangian submanifolds
论文作者
论文摘要
我们说，如果可以将其提升为$（λ^*）^n $的分析子集，则热带子变量$ v \ subset \ subset \ mathbb r^n $是$ b $ realizable。当$ v $是平滑的曲线或超出表面时，始终存在Lagrangian Submanifold Lift $ L_V \ subset（\ Mathbb C^*）^n $。我们证明，每当$ l_v $具有定义明确的浮子共同体时，我们就可以找到每个点$ v $ a lagrangian torus brane的$ v $，其Lagrangian交叉点浮子浮子共同体与$ l_v $无关。假设适用于感谢您的品种的合适同源镜对称结果，则每当$ l_v $是一个Lagrangian Submanifold时，可以通过边界的Cochain毫不掩饰，而热带亚V $ V $ IS $ B $ - $ bub-realizable。作为一种应用，我们表明，零热带曲线的拉格朗日升降是毫无开动的，从而为Nishinou和Siebert的证据提供了纯粹的符合性论证，证明了零零热带曲线为$ b $ $ - $ - 真实的。我们还证明，热带阿伯利亚表面内部的热带曲线为$ b $ - 杂货。
We say that a tropical subvariety $V\subset \mathbb R^n$ is $B$-realizable if it can be lifted to an analytic subset of $(Λ^*)^n$. When $V$ is a smooth curve or hypersurface, there always exists a Lagrangian submanifold lift $L_V\subset (\mathbb C^*)^n$. We prove that whenever $L_V$ has well-defined Floer cohomology, we can find for each point of $V$ a Lagrangian torus brane whose Lagrangian intersection Floer cohomology with $L_V$ is non-vanishing. Assuming an appropriate homological mirror symmetry result holds for toric varieties, it follows that whenever $L_V$ is a Lagrangian submanifold that can be made unobstructed by a bounding cochain, the tropical subvariety $V$ is $B$-realizable. As an application, we show that the Lagrangian lift of a genus zero tropical curve is unobstructed, thereby giving a purely symplectic argument for Nishinou and Siebert's proof that genus-zero tropical curves are $B$-realizable. We also prove that tropical curves inside tropical abelian surfaces are $B$-realizable.
