论文标题
热带Lagrangian多部门和当地自由滑轮的平滑效果
Tropical Lagrangian multi-sections and smoothing of locally free sheaves over degenerate Calabi-Yau surfaces
论文作者
论文摘要
我们介绍了热带拉格朗日多区域的概念，上面是$ 2 $维的积分仿射歧管$ b $带有奇异性的概念，并使用它们来研究卡拉比雅表面上较高等级的重建问题。在某些热带拉格朗日多段$ \ mathbb {l} $上面的$ B $上，这些$ b $是通过在分支上的局部模型中明确构建的，我们构建本地免费的sheaves $ \ mathcal {e} _0（e} _0（\ mathbb {\ mathb {l}，{\ bf {\ bf {\ bf { $ x_0（B，\ Mathscr {p}，S）$与配备了多面体分解$ \ Mathscr {p} $的$ b $相关的$。然后，我们在这样的$ \ mathbb {l} $上找到组合条件，在该条件下，捆绑$ \ mathcal {e} _0（\ mathbb {l}，{\ bf {k}} _ s）$很简单。这会产生可平滑对的明确示例$（x_0（x_0（b，\ mathscr {p}，s），\ Mathcal {e} _0（\ Mathbb {l}，{\ bf {k}} _ s _ s _ s _ s _ s））$在dimension 2中。
We introduce the notion of tropical Lagrangian multi-sections over a $2$-dimensional integral affine manifold $B$ with singularities, and use them to study the reconstruction problem for higher rank locally free sheaves over Calabi-Yau surfaces. To certain tropical Lagrangian multi-sections $\mathbb{L}$ over $B$, which are explicitly constructed by prescribing local models around the ramification points, we construct locally free sheaves $\mathcal{E}_0(\mathbb{L},{\bf{k}}_s)$ over the singular projective scheme $X_0(B,\mathscr{P},s)$ associated to $B$ equipped with a polyhedral decomposition $\mathscr{P}$ and a gluing data $s$. We then find combinatorial conditions on such an $\mathbb{L}$ under which the sheaf $\mathcal{E}_0(\mathbb{L},{\bf{k}}_s)$ is simple. This produces explicit examples of smoothable pairs $(X_0(B,\mathscr{P},s),\mathcal{E}_0(\mathbb{L},{\bf{k}}_s))$ in dimension 2.
