相关论文: Quotients of E^n by A_{n+1} and Calabi-Yau manifol…

We solve $\mathcal{N}=1$ supersymmetric $A_{2}$ type $U(N)\times U(N)$ matrix models obtained by deforming $\mathcal{N}=2$ with symmetric tree level superpotentials of any degree exactly in the planar limit. These theories can be…

We present a complete intersection Calabi-Yau manifold Y that has Euler number -72 and which admits free actions by two groups of automorphisms of order 12. These are the cyclic group Z_12 and the non-Abelian dicyclic group Dic_3. The…

We study punctual quot-schemes of torsion-free sheaves $E_Y$ on smooth projective curves, surfaces and Calabi--Yau fourfolds via their virtual geometry. Our goal is to give a complete description of the virtual fundamental classes and their…

Let $M$ be a complete Ricci-flat Kahler manifold with one end and assume that this end converges at an exponential rate to $[0,\infty) \times X$ for some compact connected Ricci-flat manifold $X$. We begin by proving general structure…

In this work we study the quantum periods together with their Picard-Fuchs differential equations of Calabi-Yau fourfolds. In contrast to Calabi-Yau threefolds, we argue that the large volume points of Calabi-Yau fourfolds generically are…

We consider graded twisted Calabi-Yau algebras of dimension 3 which are derivation-quotient algebras of the form $A = \kk Q/I$, where $Q$ is a quiver and $I$ is an ideal of relations coming from taking partial derivatives of a twisted…

We explicitly construct the Kummer variety associated to the Jacobian of a hyperelliptic curve of genus 3 that is defined over a field of characteristic not equal to 2 and has a Weierstra{\ss} point defined over the same field. We also…

The open string sector of the topological B-model on CY $(m+2)$-folds is described by $m$-graded quivers with superpotentials. This correspondence generalizes the connection between CY $(m+2)$-folds and gauge theories on the worldvolume of…

The aim of this paper is to analyze some geometric properties of the rigid Calabi--Yau threefold $\mathcal{Z}$ obtained by a quotient of $E^3$, where $E$ is a specific elliptic curve. We describe the cohomology of $\mathcal{Z}$ and give a…

In this note, an overview of Calabi-Yau varieties in positive characteristic is presented. Although Calabi-Yau varieties in characteristic zero are unobstructed, there are examples of Calabi-Yau threefolds in positive characteristic which…

To every elliptic Calabi-Yau threefold with a section $X$ there can be associated a Lie group $G$ and a representation $\rho$ of that group. The group is determined from the Weierstrass model, which has singularities that are generically…

This paper describes the reconstruction of the topological string partition function for certain local Calabi-Yau (CY) manifolds from the quantum curve, an ordinary differential equation obtained by quantising their defining equations.…

We use the representation theory of N=2 superconformal algebra to study the elliptic genera of Calabi-Yau (CY) D-folds. We compute the entropy of CY manifolds from the growth rate of multiplicities of the massive (non-BPS) representations…

We define an iterative construction that produces a family of elliptically fibered Calabi-Yau $n$-folds with section from a family of elliptic Calabi-Yau varieties of one dimension lower. Parallel to the geometric construction, we…

In the present work the local form of certain Calabi-Yau metrics possessing a local Hamiltonian Killing vector is described in terms of a single non linear equation. The main assumptions are that the complex $(3,0)$-form is of the form…

I construct some smooth Calabi-Yau threefolds in characteristic two and three that do not lift to characteristic zero. These threefolds are pencils of supersingular K3-surfaces. The construction depends on Moret-Bailly's pencil of abelian…

Degenerate contributions to higher genus Gromov-Witten invariants of Calabi-Yau 3-folds are computed via Hodge integrals. The vanishing of contributions of covers of elliptic curves conjectured by Gopakumar and Vafa is proven. A formula for…

Let X be the toric variety (P^1)^4 associated with its four-dimensional polytope. Consider a resolution of the singular Fano variety associated with the dual polytope of X. Generically, anti-canonical sections Y of X and anticanonical…

In this paper, we are able to prove an analogy of the Calabi-Yau theorem for complete Riemannian manifolds with nonnegative scalar curvature which are aspherical at infinity. The key tool is an existence result for arbitrarily large bounded…

The Castelnuovo bound conjecture, which is proposed by physicists, predicts an effective vanishing result for Gopakumar-Vafa invariants of Calabi-Yau 3-folds of Picard number one. Previously, it is only known for a few cases and all the…