Monodromy of monomially admissible Fukaya-Seidel categories mirror to toric varieties
TLDR
In this article, a monodromy action on the monomially admissible Fukaya-Seidel categories of these Laurent polynomials was shown, as the arguments of their coefficients vary that corresponds under homological mirror symmetry to tensoring by a line bundle naturally associated to monomials whose coefficients are rotated.About:
This article is published in Advances in Mathematics.The article was published on 2019-07-09 and is currently open access. It has received 18 citations till now. The article focuses on the topics: Toric variety & Homological mirror symmetry.read more
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Homological mirror symmetry for log Calabi-Yau surfaces
Paul Hacking,Ailsa Keating +1 more
TL;DR: In this paper, the authors constructed a mirror Lefschetz fibration for a log Calabi-Yau surface with a distinguished complex structure, such that the directed Fukaya category of $w$ is isomorphic to $D^b \text{Coh}(Y)$ and the wrapped Fukaya categories of $m$ is also isomorphic with respect to the total space of the almost toric fibration arising in the work of Gross-Hacking-Keel.
Journal ArticleDOI
Tropical Lagrangian Hypersurfaces are Unobstructed
TL;DR: For each tropical hypersurface, the moment map projection of a tropical amoeba of a Lagrangian is a toric mirror to sheaves supported on complex hypersurfaces as discussed by the authors.
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Kasteleyn operators from mirror symmetry
TL;DR: In this paper, it was shown that tensoring with line bundles on the compactification is mirror to certain Legendrian autoisotopies of the asymptotic boundary of the Lagrangian.
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Tropical Lagrangian hypersurfaces are unobstructed
TL;DR: For each tropical hypersurface, the moment map projection of a tropical amoeba of a Lagrangian is a toric mirror to sheaves supported on complex hypersurfaces as discussed by the authors.
Journal ArticleDOI
The Gamma and Strominger-Yau-Zaslow conjectures: a tropical approach to periods
TL;DR: In this paper, a new method to compute asymptotics of periods using tropical geometry is proposed, in which the Riemann zeta values appear naturally as error terms in tropicalization.
References
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Proceedings ArticleDOI
Homological mirror symmetry and torus fibrations
Maxim Kontsevich,Yan Soibelman +1 more
TL;DR: In this article, the Strominger-Yau-Zaslow conjecture about torus fibrations and the homological mirror conjecture about an equivalence of the Fukaya category of a Calabi Yau manifold and the derived category of coherent sheaves on the dual CalabiYau manifold were discussed.
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Functors and Computations in Floer homology with Applications Part II
TL;DR: In this article, it was shown that the Floer cohomology of the cotangent bundle is isomorphic to the cohomologies of the loop space of the base.
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Graded lagrangian submanifolds
TL;DR: The notion de sous-variete Lagrangienne graduee sert a lever cette ambiguite as mentioned in this paper, a notion of cohomologie de Floer symplectique.