Lagrangian Floer theory on compact toric manifolds, I

K Fukaya, YG Oh, H Ohta, K Ono - 2010 - projecteuclid.org
We introduced the notion of weakly unobstructed Lagrangian submanifolds and constructed
their potential function (PO) purely in terms of A-model data in [FOOO3]. In this article, we …

Mirror symmetry for del Pezzo surfaces: vanishing cycles and coherent sheaves

D Auroux, L Katzarkov, D Orlov - Inventiones mathematicae, 2006 - Springer
We study homological mirror symmetry for Del Pezzo surfaces and their mirror Landau-
Ginzburg models. In particular, we show that the derived category of coherent sheaves on a …

Brane tilings and their applications

M Yamazaki - Fortschritte der Physik: Progress of Physics, 2008 - Wiley Online Library
We review recent developments in the theory of brane tilings and four‐dimensional 𝒩= 1
supersymmetric quiver gauge theories. This review consists of two parts. In part I, we …

Homological mirror symmetry for punctured spheres

M Abouzaid, D Auroux, A Efimov, L Katzarkov… - Journal of the American …, 2013 - ams.org
We prove that the wrapped Fukaya category of a punctured sphere ($ S^{2} $ with an
arbitrary number of points removed) is equivalent to the triangulated category of singularities …

Homological mirror symmetry for log Calabi–Yau surfaces

P Hacking, A Keating - Geometry & Topology, 2023 - msp.org
Abstract 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→ ℂ, where …

T-duality and homological mirror symmetry for toric varieties

B Fang, CCM Liu, D Treumann, E Zaslow - Advances in Mathematics, 2012 - Elsevier
Let XΣ be a complete toric variety. The coherent-constructible correspondence κ of Fang et
al.(2011)[14] equates PerfT (XΣ) with a subcategory Shcc (MR; ΛΣ) of constructible sheaves …

The nonequivariant coherent-constructible correspondence for toric stacks

T Kuwagaki - 2020 - projecteuclid.org
The nonequivariant coherent-constructible correspondence is a microlocal-geometric
interpretation of homological mirror symmetry for toric varieties conjectured by Fang, Liu …

[PDF][PDF] Mirror symmetry for toric Fano manifolds via SYZ transformations

K Chan, NC Leung - arXiv preprint arXiv:0801.2830, 2008 - arxiv.org
arXiv:0801.2830v4 [math.SG] 1 Oct 2009 Page 1 arXiv:0801.2830v4 [math.SG] 1 Oct 2009
MIRROR SYMMETRY FOR TORIC FANO MANIFOLDS VIA SYZ TRANSFORMATIONS …

Suspending Lefschetz fibrations, with an application to local mirror symmetry

P Seidel - Communications in Mathematical Physics, 2010 - Springer
We describe the behaviour of Fukaya categories under “suspension”, which means passing
from the fibre of a Lefschetz fibration to the double cover of the total space branched along …

The coherent–constructible correspondence for toric Deligne–Mumford stacks

B Fang, CCM Liu, D Treumann… - International …, 2014 - ieeexplore.ieee.org
We extend our previous work 8 on coherent–constructible correspondence for toric varieties
to toric Deligne–Mumford (DM) stacks. Following Borisov et al. 3, a toric DM stack …