Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homological mirror symmetry for log Calabi-Yau surfaces   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.

10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an