10 citations · 34 across the 15 of their papers we have counts for
18 papers
Mirror symmetry for gCICY threefolds (I): a block and a non-Gorenstein toric phase
Atsushi Kanazawa
We construct and analyze a mirror family for the generalized complete intersection Calabi-Yau threefold , with $(h^{1,1},h^{…
Mirror symmetry for gCICY threefolds (II): blocks, VGIT, and toric phases
Atsushi Kanazawa
The configuration matrices of generalized complete intersection Calabi-Yau (gCICY) threefolds contain negative entries, so their defining line bundles are not nef and the Batyrev-B…
Chern bounds and tangent geometry of polarized Calabi-Yau threefolds
Atsushi Kanazawa
We study the numerical geography and tangent geometry of very amply polarized Calabi--Yau threefolds through the positivity of the first jet bundle . Writing $d=\in…
BCOV cusp forms of lattice polarized K3 surfaces
Shinobu Hosono, Atsushi Kanazawa
We introduce the BCOV formula for the lattice polarized K3 surfaces. We find that it yields cusp forms expressed by certain eta products for many families of rank 19 lattice polari…
Attractor mechanisms of moduli spaces of Calabi-Yau 3-folds
Yu-Wei Fan, Atsushi Kanazawa
We investigate the complex and Kähler attractor mechanisms of moduli spaces of Calabi-Yau 3-folds. The complex attractor mechanism was previously studied by Ferrara-Kallosh-Stromin…
Mirror symmetry and rigid structures of generalized K3 surfaces
Atsushi Kanazawa
The present article is concerned with mirror symmetry for generalized K3 surfaces, with particular emphasis on complex and Kähler rigid structures. Inspired by the works of Dolgach…
Degenerations and Lagrangian fibrations of Calabi-Yau manifolds
Atsushi Kanazawa
We discuss various topics on degenerations and special Lagrangian torus fibrations of Calabi-Yau manifolds in the context of mirror symmetry. A particular emphasis is on Tyurin deg…
Weil-Petersson geometry on the space of Bridgeland stability conditions
Yu-Wei Fan, Atsushi Kanazawa, Shing-Tung Yau
Inspired by mirror symmetry, we investigate some differential geometric aspects of the space of Bridgeland stability conditions on a Calabi-Yau triangulated category. The aim is to…
Doran-Harder-Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves
Atsushi Kanazawa
We prove the Doran-Harder-Thompson conjecture in the case of elliptic curves by using ideas from SYZ mirror symmetry. The conjecture claims that when a Calabi-Yau manifold dege…
Local Calabi-Yau manifolds of type \tilde{A} via SYZ mirror symmetry
Atsushi Kanazawa, Siu-Cheong Lau
We carry out the SYZ program for the local Calabi--Yau manifolds of type by developing an equivariant SYZ theory for the toric Calabi--Yau manifolds of infinite-typ…
Calabi-Yau threefolds of type K (II): Mirror symmetry
Kenji Hashimoto, Atsushi Kanazawa
A Calabi-Yau threefold is called of type K if it admits an étale Galois covering by the product of a K3 surface and an elliptic curve. In our previous paper, based on Oguiso-Sakura…
Geometric transitions and SYZ mirror symmetry
Atsushi Kanazawa, Siu-Cheong Lau
We prove that the punctured generalized conifolds and punctured orbifolded conifolds are mirror symmetric under the SYZ program with quantum corrections. This mathematically confir…
Non-commutative projective Calabi-Yau schemes
Atsushi Kanazawa
The objective of the present article is to construct the first examples of (non-trivial) non-commutative projective Calabi-Yau schemes in the sense of Artin and Zhang.
Calabi-Yau threefolds of type K (I): Classification
Kenji Hashimoto, Atsushi Kanazawa
Any Calabi-Yau threefold X with infinite fundamental group admits an étale Galois covering either by an abelian threefold or by the product of a K3 surface and an elliptic curve. W…
Lectures on BCOV holomorphic anomaly equations
Atsushi Kanazawa, Jie Zhou
The present article surveys some mathematical aspects of the BCOV holomorphic anomaly equations introduced by Bershadsky, Cecotti, Ooguri and Vafa. It grew from a series of lecture…
Degenerating Hodge structure of one-parameter family of Calabi-Yau threefolds
Tatsuki Hayama, Atsushi Kanazawa
To a one-parameter family of Calabi-Yau threefolds, we can associate the extended period map by the log Hodge theory of Kato and Usui. In the present paper, we study the image of a…
Trilinear forms and Chern classes of Calabi-Yau threefolds
Atsushi Kanazawa, P. M. H. Wilson
Let X be a Calabi-Yau threefold and μthe symmetric trilinear form on the second cohomology group H^{2}(X,\Z) defined by the cup product. We investigate the interplay between the Ch…
Pfaffian Calabi-Yau Threefolds and Mirror Symmetry
Atsushi Kanazawa
The aim of this article is to report on recent progress in understanding mirror symmetry for some non-complete intersection Calabi-Yau threefolds. We first construct four new smoot…