About Homological Mirror Symmetry
A Imparato - arXiv preprint arXiv:2306.13589, 2023 - arxiv.org
The B-side of Kontsevich's Homological Mirror Symmetry Conjecture is discussed. We give
first a self-contained study of derived categories and their homological algebra, and later …
first a self-contained study of derived categories and their homological algebra, and later …
An introduction to homological mirror symmetry and the case of elliptic curves
A Port - arXiv preprint arXiv:1501.00730, 2015 - arxiv.org
Here we carefully construct an equivalence between the derived category of coherent
sheaves on an elliptic curve and a version of the Fukaya category on its mirror. This is the …
sheaves on an elliptic curve and a version of the Fukaya category on its mirror. This is the …
Mirror symmetry: from categories to curve counts
S Ganatra, T Perutz, N Sheridan - arXiv preprint arXiv:1510.03839, 2015 - arxiv.org
We work in the setting of Calabi-Yau mirror symmetry. We establish conditions under which
Kontsevich's homological mirror symmetry (which relates the derived Fukaya category to the …
Kontsevich's homological mirror symmetry (which relates the derived Fukaya category to the …
[图书][B] From primitive forms to Frobenius manifolds
K Saito, A Takahashi - 2008 - kurims.kyoto-u.ac.jp
In early 1980'th, the first named author, in the study of the period map associated with a
primitive form [S3, S4], found certain differential geometric structure on the base space of a …
primitive form [S3, S4], found certain differential geometric structure on the base space of a …
Towards Homological Mirror Symmetry
A Imparato - arXiv preprint arXiv:2108.03931, 2021 - arxiv.org
This is an expository article on the A-side of Kontsevich's Homological Mirror Symmetry
conjecture. We give first a self-contained study of $ A_\infty $-categories and their …
conjecture. We give first a self-contained study of $ A_\infty $-categories and their …
Categorical mirror symmetry: the elliptic curve
A Polishchuk, E Zaslow - arXiv preprint math/9801119, 1998 - arxiv.org
We describe an isomorphism of categories conjectured by Kontsevich. If $ M $ and
$\widetilde {M} $ are mirror pairs then the conjectural equivalence is between the derived …
$\widetilde {M} $ are mirror pairs then the conjectural equivalence is between the derived …
Homological mirror symmetry with higher products
A Polishchuk - arXiv preprint math/9901025, 1999 - arxiv.org
We construct an $ A_ {\infty} $-structure on the Ext-groups of hermitian holomorphic vector
bundles on a compact complex manifold. We propose a generalization of the homological …
bundles on a compact complex manifold. We propose a generalization of the homological …
[PDF][PDF] Mirror symmetry and K3 surfaces
K Ueda - arXiv preprint arXiv:1407.1566, 2014 - arxiv.org
Mirror symmetry is a mysterious relationship, originally suggested by string theorists,
between symplectic geometry of one Calabi-Yau manifold and complex geometry of another …
between symplectic geometry of one Calabi-Yau manifold and complex geometry of another …
Categorical mirror symmetry on cohomology for a complex genus 2 curve
C Cannizzo - Advances in Mathematics, 2020 - Elsevier
Motivated by observations in physics, mirror symmetry is the concept that certain manifolds
come in pairs X and Y such that the complex geometry on X mirrors the symplectic geometry …
come in pairs X and Y such that the complex geometry on X mirrors the symplectic geometry …
Homological mirror symmetry in dimension one
B Kreußler - arXiv preprint math/0012018, 2000 - arxiv.org
In this paper we complete the proof began by A. Polishchuk and E. Zaslow (math.
AG/9801119) of a weak version of Kontsevich's homological mirror symmetry conjecture for …
AG/9801119) of a weak version of Kontsevich's homological mirror symmetry conjecture for …