相关论文: Geometrical McKay Correspondence for Isolated Sing…
This paper discusses the overlap of the Hori-Vafa formulation of mirror symmetry with some other constructions. We focus on compact Calabi-Yau hypersurfaces \mathcal{M}_G = {G = 0} in weighted complex projective spaces. The Hori-Vafa…
We construct an algebraic variety by resolving singularities of a quintic Calabi-Yau threefold. The middle cohomology of the threefold is shown to contain a piece coming from a pair of elliptic surfaces. The resulting quotient is a…
We study mirror symmetry of Calabi-Yau manifolds within the framework of the Gauss-Manin system. Applying the flat coordinates to the Gauss-Manin system for the periods, we derive differential equations for the mirror map in addition to the…
Let $A$ be an abelian variety, and $G \subset Aut(A)$ a finite group acting freely in codimension two. We discuss whether the singular quotient $A/G$ admits a resolution that is a Calabi-Yau manifold. While Oguiso constructed two examples…
We provide a uniform solution to 4d N=2 gauge theory with a single gauge group G=A,D,E when the one-loop contribution to the beta function from any irreducible component R of the hypermultiplets is less than or equal to half of that of the…
We use the differential geometrical framework of generalized (almost) Calabi-Yau structures to reconsider the concept of mirror symmetry. It is shown that not only the metric and B-field but also the algebraic structures are uniquely…
We give close formulas for the counting functions of rational curves on complete intersection Calabi-Yau manifolds in terms of special solutions of generalized hypergeometric differential systems. For the one modulus cases we derive a…
We describe local mirror symmetry from a mathematical point of view and make several A-model calculations using the mirror principle (localization). Our results agree with B-model computations from solutions of Picard-Fuchs differential…
We announce a result on quantum McKay correspondence for disc invariants of outer legs in toric Calabi-Yau 3-orbifolds, and illustrate our method in a special example $[\mathbb C^3 /\mathbb Z_5 (1, 1, 3)]$.
Let $G$ be a finite subgroup of $\mathrm{SU}(4)$ whose elements have age not larger than one. In the first part of this paper, we define $K$-theoretic stable pair invariants on the crepant resolution of the affine quotient $\mathbb{C}^4/G$,…
A Calabi-Yau threefold is called of type K if it admits an \'etale Galois covering by the product of a K3 surface and an elliptic curve. In our previous paper, based on Oguiso-Sakurai's fundamental work, we provide the full classification…
We obtain mirror formulas for the genus 1 Gromov-Witten invariants of projective Calabi-Yau complete intersections. We follow the approach previously used for projective hypersurfaces by extending the scope of its algebraic results; there…
We describe pretty examples of derived equivalences and autoequivalences of Calabi-Yau threefolds arising from pencils of cubic fourfolds. The cubic fourfolds are chosen to be special, so they have an associated K3 surface. Thus a pencil…
For $n\geq 1$, we construct the Hilbert scheme of $n$ points on any crepant partial resolution of a Kleinian singularity as a Nakajima quiver variety for an explicit GIT stability parameter. This generalises and unifies existing quiver…
In this work, we present a new geometric transition in non-compact Calabi-Yau 4-folds, specifically for the cone over the 7d Sasaki-Einstein manifold $Q^{\scriptscriptstyle(1,1,1)}/\mathbb{Z}_{N}$. We discover a new smoothing of such…
At special loci in their moduli spaces, Calabi-Yau manifolds are endowed with discrete symmetries. Over the years, such spaces have been intensely studied and have found a variety of important applications. As string compactifications they…
A numerical framework for approximating $\mathrm{G}_2$-structure 3-forms on contact Calabi-Yau manifolds is presented. The approach proceeds in three stages: first, existing neural network models are employed to compute an approximate…
The recent result of Strominger, Yau and Zaslow relating mirror symmetry to the quantum field theory notion of T-duality is reinterpreted as providing a way of geometrically characterizing which Calabi-Yau manifolds have mirror partners.…
By generalizing the Landau-Ginzburg/Calabi-Yau correspondence for hypersurfaces, we can relate a Calabi-Yau complete intersection to a hybrid Landau-Ginzburg model: a family of isolated singularities fibered over a projective line. In…
Any irreducible Dynkin diagram $\Delta$ is obtained from an irreducible Dynkin diagram $\Delta_h$ of type $\mathrm{ADE}$ by folding via graph automorphisms. For any simple complex Lie group $G$ with Dynkin diagram $\Delta$ and compact…