116 citations · 459 across the 20 of their papers we have counts for
24 papers
Symplectomorphisms of some Weinstein 4-manifolds
Paul Hacking, Ailsa Keating
Let M be a Weinstein four-manifold mirror to Y\D for (Y,D) a log Calabi--Yau surface; intuitively, this is typically the Milnor fibre of a smoothing of a cusp singularity. We intro…
Secondary fan, theta functions and moduli of Calabi-Yau pairs
Paul Hacking, Sean Keel, Tony Yue Yu
We conjecture that any connected component of the moduli space of triples where is a smooth projective variety, is a normal crossing anti-canoni…
Homological mirror symmetry for log Calabi-Yau surfaces
Paul Hacking, Ailsa Keating, Wendelin Lutz
Given a log Calabi-Yau surface with maximal boundary and distinguished complex structure, we explain how to construct a mirror Lefschetz fibration , wh…
The mirror of the cubic surface
Mark Gross, Paul Hacking, Sean Keel +1
This paper expands on a remark in the paper "Mirror Symmetry for Log Calabi-Yau Surfaces I" of the first three authors of this paper, explaining fully how various constructions of…
Theta functions on varieties with effective anti-canonical class
Mark Gross, Paul Hacking, Bernd Siebert
We show that a large class of maximally degenerating families of n-dimensional polarized varieties come with a canonical basis of sections of powers of the ample line bundle. The f…
Canonical bases for cluster algebras
Mark Gross, Paul Hacking, Sean Keel +1
In previous work, the first three authors conjectured that the ring of regular functions on a natural class of affine log Calabi-Yau varieties (those with maximal boundary) has a c…