论文标题
log calabi-yau表面的同源镜对称性
Homological mirror symmetry for log Calabi-Yau surfaces
论文作者
论文摘要
给定带有最大边界$ d $的log calabi-yau表面$ y $和杰出的复杂结构，我们解释了如何构建镜子lefschetz纤维$ w：m w：m \ to \ sathbb {c} $，其中$ m $是weinstein fourd-manifold包装的Fukaya类别$ d^b \ Mathcal {w}（m）$是同构至$ d^b \ text {coh}（y \ backslash d）$。我们在$ m $和几乎是振动的总空间之间构建了明显的同构，这是在毛keel的工作中产生的。当$ d $是负面的时，预计这将是$ d $的双尖的米尔诺纤维。我们还将镜子的潜在$ w $与现有构造的一系列特殊案例（y，d）$相匹配，尤其是在Auroux-Katzarkov-Orlov和Abouzaid的工作中。
Given a log Calabi-Yau surface $Y$ with maximal boundary $D$ and distinguished complex structure, we explain how to construct a mirror Lefschetz fibration $w: M \to \mathbb{C}$, where $M$ is a Weinstein four-manifold, such that the directed Fukaya category of $w$ is isomorphic to $D^b \text{Coh}(Y)$, and the wrapped Fukaya category $D^b\mathcal{W} (M)$ is isomorphic to $D^b \text{Coh}(Y \backslash D)$. We construct an explicit isomorphism between $M$ and the total space of the almost-toric fibration arising in the work of Gross-Hacking-Keel; when $D$ is negative definite this is expected to be the Milnor fibre of a smoothing of the dual cusp of $D$. We also match our mirror potential $w$ with existing constructions for a range of special cases of $(Y,D)$, notably in work of Auroux-Katzarkov-Orlov and Abouzaid.
