Related papers: Resolved Toroidal Orbifolds and their Orientifolds
Most of Calabi-Yau manifolds that have been considered by physicists are complete intersection Calabi-Yau manifolds of toric varieties or some quotients of product types. Purpose of this paper is to introduce a different and rather new kind…
We exhibit examples of pairs $(X,D)$ where $X$ is a smooth projective variety and $D$ is an anticanonical reduced simple normal crossing divisor such that the deformations of $(X,D)$ are obstructed. These examples are constructed via toric…
In this paper we establish a necessary and sufficient condition for solving a general class of fully nonlinear elliptic equations on compact almost Hermitian manifolds, extending a recent work of Guo-Song. As applications, we determine the…
We investigate the mathematical properties of the class of Calabi-Yau four-folds recently found in [arXiv:1303.1832]. This class consists of 921,497 configuration matrices which correspond to manifolds that are described as complete…
C. Voisin and C. Borcea have constructed mirror pairs of families of Calabi-Yau threefolds by taking the quotient of the product of an elliptic curve with a K3 surface endowed with a non-symplectic involution. In this paper, we generalize…
In this paper, we study the form type Calabi-Yau equation. We define the astheno-Ricci curvature and prove that there exists a solution for the form type Calabi-Yau equation if the astheno-Ricci curvature is non-positive.
The Poincare conjecture is analyzed in the context of Calabi-Yau $n$-folds. A simple treatment is given by embedding the three-manifolds into these CY manifolds, and then taking the orbifold limit. The higher-dimensional proofs are also…
We review three methods of counting abelian orbifolds of the form C^3/Gamma which are toric Calabi-Yau (CY). The methods include the use of 3-tuples to define the action of Gamma on C^3, the counting of triangular toric diagrams and the…
In this note, a procedure is developed to explicitly construct non-trivial F-theory lifts of perturbative IIB orientifold models on Calabi-Yau complete intersections in toric varieties. This procedure works on Calabi-Yau orientifolds where…
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 describe two ways to construct finite rational morphisms between fiber products of rational elliptic surfaces with section and some Calabi--Yau manifolds. We use them to construct correspondences between such fiber products that admit at…
We introduce orbifold Euler numbers for normal surfaces with Q-divisors. These numbers behave multiplicatively under finite maps and in the log canonical case we prove that they satisfy the Bogomolov-Miyaoka-Yau type inequality. As a…
We investigate topological properties of Calabi-Yau fourfolds and consider a wide class of explicit constructions in weighted projective spaces and, more generally, toric varieties. Divisors which lead to a non-perturbative superpotential…
A primitive Calabi-Yau threefold is a non-singular Calabi-Yau threefold which cannot be written as a crepant resolution of a singular fibre of a degeneration of Calabi-Yau threefolds. These should be thought as the most basic Calabi-Yau…
Using the Kreuzer-Skarke database of 4-dimensional reflexive polytopes, we systematically constructed a new database of orientifold Calabi-Yau threefolds with $h^{1,1}(X) \leq 12$. Our approach involved non-trivial $\mathbb{Z}_2$…
We define Donaldson-Thomas invariants of Calabi-Yau orbifolds and we develop a topological vertex formalism for computing them. The basic combinatorial object is the orbifold vertex, a generating function for the number of 3D partitions…
The aim of this article is to give a method to construct bimodule resolutions of associative algebras, generalizing Bardzell's well-known resolution of monomial algebras. We stress that this method leads to concrete computations, providing…
Various methods to find Calabi-Yau differential equations are discussed.
There are easy "polynomial" deformations of Calabi-Yau hypersurfaces in toric varieties performed by changing the coefficients of the defining polynomial of the hypersurface. In this paper, we explicitly constructed the ``non-polynomial''…
We compute numerical approximations of the period integrals for eleven rigid double octic Calabi--Yau threefolds and compare them with the periods of corresponding weight our cusp forms and find, as to be expected, commensurabilities. These…