Hodge theoretic aspects of mirror symmetry
L Katzarkov, M Kontsevich, T Pantev - arXiv preprint arXiv:0806.0107, 2008 - arxiv.org
We discuss the Hodge theory of algebraic non-commutative spaces and analyze how this
theory interacts with the Calabi-Yau condition and with mirror symmetry. We develop an …
theory interacts with the Calabi-Yau condition and with mirror symmetry. We develop an …
Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces
M Abouzaid, D Auroux, L Katzarkov - Publications mathématiques de l' …, 2016 - Springer
We consider mirror symmetry for (essentially arbitrary) hypersurfaces in (possibly
noncompact) toric varieties from the perspective of the Strominger-Yau-Zaslow (SYZ) …
noncompact) toric varieties from the perspective of the Strominger-Yau-Zaslow (SYZ) …
[PDF][PDF] Homological mirror symmetry for hypersurfaces in (C∗) n
M Abouzaid, D Auroux - arXiv preprint arXiv:2111.06543, 2021 - people.math.harvard.edu
We prove a homological mirror symmetry result for maximally degenerating families of
hypersurfaces in (C∗) n (B-model) and their mirror toric Landau-Ginzburg A-models. The …
hypersurfaces in (C∗) n (B-model) and their mirror toric Landau-Ginzburg A-models. The …
Global matrix factorizations
KH Lin, D Pomerleano - arXiv preprint arXiv:1101.5847, 2011 - arxiv.org
We study matrix factorization and curved module categories for Landau-Ginzburg models (X,
W) with X a smooth variety, extending parts of the work of Dyckerhoff. Following Positselski …
W) with X a smooth variety, extending parts of the work of Dyckerhoff. Following Positselski …
Towards mirror symmetry for varieties of general type
M Gross, L Katzarkov, H Ruddat - Advances in Mathematics, 2017 - Elsevier
The goal of this paper is to propose a theory of mirror symmetry for varieties of general type.
Using Landau–Ginzburg mirrors as motivation, we describe the mirror of a hypersurface of …
Using Landau–Ginzburg mirrors as motivation, we describe the mirror of a hypersurface of …
[HTML][HTML] A category of kernels for equivariant factorizations, II: further implications
We leverage the results of the prequel [8], in combination with a theorem of D. Orlov to
create a categorical covering picture for factorizations. As applications, we provide a …
create a categorical covering picture for factorizations. As applications, we provide a …
[HTML][HTML] Derived categories of BHK mirrors
We prove a derived analogue to the results of Borisov, Clarke, Kelly, and Shoemaker on the
birationality of Berglund-Hübsch-Krawitz mirrors. Heavily bootstrapping off work of Seidel …
birationality of Berglund-Hübsch-Krawitz mirrors. Heavily bootstrapping off work of Seidel …
Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces
M Abouzaid, D Auroux, L Katzarkov - arXiv preprint arXiv:1205.0053, 2012 - arxiv.org
We consider mirror symmetry for (essentially arbitrary) hypersurfaces in (possibly
noncompact) toric varieties from the perspective of the Strominger-Yau-Zaslow (SYZ) …
noncompact) toric varieties from the perspective of the Strominger-Yau-Zaslow (SYZ) …
Birationality of Berglund–Hübsch–Krawitz mirrors
M Shoemaker - Communications in Mathematical Physics, 2014 - Springer
Birationality of Berglund–Hübsch–Krawitz Mirrors Page 1 Digital Object Identifier (DOI)
10.1007/s00220-014-2121-y Commun. Math. Phys. 331, 417–429 (2014) Communications …
10.1007/s00220-014-2121-y Commun. Math. Phys. 331, 417–429 (2014) Communications …
A global mirror symmetry framework for the Landau–Ginzburg/Calabi–Yau correspondence
A Chiodo, Y Ruan - Annales de l'Institut Fourier, 2011 - numdam.org
We survey FJRW theory introduced by Fan, Jarvis, and the second author for the Landau–
Ginzburg model following ideas of Witten. We review its connection to related work and we …
Ginzburg model following ideas of Witten. We review its connection to related work and we …