Related papers: Calabi-Yau conifold expansions
We describe a variation of Dworks unit-root method to determine the degree four Frobenius polynomial for members of a 1-modulus Calabi-Yau family over $\mathbb{P}^1$ in terms of the holomorphic period near a point of maximal unipotent…
We consider a geometric regularization for the class of conifold transitions relating D-brane systems on noncompact Calabi-Yau spaces to certain flux backgrounds. This regularization respects the SL(2,Z) invariance of the flux…
Compactifications with fluxes and branes motivate us to study various enumerative invariants of Calabi-Yau manifolds. In this paper, we study non-perturbative corrections depending on both open and closed string moduli for a class of…
We investigate a method of construction of Calabi--Yau manifolds, that is, by smoothing normal crossing varieties. We develop some theories for calculating the Picard groups of the Calabi--Yau manifolds obtained in this method. Some…
We study the set of rational curves of a certain topological type in general members of certain families of Calabi-Yau threefolds. For some families we investigate to what extent it is possible to conclude that this set is finite. For other…
The moduli space of multiply-connected Calabi-Yau threefolds is shown to contain codimension-one loci on which the corresponding variety develops a certain type of hyperquotient singularity. These have local descriptions as discrete…
Motivated by mirror symmetry of one-parameter models, an interesting class of Fuchsian differential operators can be singled out, the so-called Calabi--Yau operators, introduced by Almkvist and Zudilin. They conjecturally determine…
We propose an extended set of differential operators for local mirror symmetry. If $X$ is Calabi-Yau such that $\dim H_4(X,\Z)=0$, then we show that our operators fully describe mirror symmetry. In the process, a conjecture for intersection…
We explore the landscape of F-theory compactifications on Calabi--Yau fourfolds whose complex structure moduli space is the thrice-punctured sphere. As a first part, we enumerate all such Calabi--Yau fourfolds under the additional…
We analyse the family of Calabi-Yau varieties attached to four-point fishnet integrals in two dimensions. We find that the Picard-Fuchs operators for fishnet integrals are exterior powers of the Picard-Fuchs operators for ladder integrals.…
In this paper we mainly study Calabi-Yau varieties that arise as triple covers of products of projective lines branched along simple normal crossing divisors. For some of those families of Calabi-Yau varieties, the period maps factor…
Using the prescription of [1] for defining period integrals in the Landau-Ginsburg theory for compact Calabi-Yau's, we obtain the Picard-Fuchs equation and the Meijer basis of solutions for the compact Calabi-Yau CY_3(3,243) expressed 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…
In this note we speculate about the structure of maximal product subvarieties in moduli stacks of Calabi-Yau manifolds. We discuss examples for quintic hypersurfaces in the four dimensional projective space.
In this article, we study the orbifold fundamental group $\pi_1^{\rm orb}(X,\Delta)$ of a Calabi--Yau pair $(X,\Delta)$ with log canonical singularities. We conjecture that the orbifold fundamental group $\pi_1^{\rm orb}(X,\Delta)$ of a…
The period geometry of Calabi-Yau $n$-folds, characterised by their variations of Hodge structure governed by Griffiths transversality, a graded Frobenius algebra, an integral monodromy and an intriguing arithmetic structure, is analysed…
For compact Calabi-Yau geometries with D5-branes we study N=1 effective superpotentials depending on both open- and closed-string fields. We develop methods to derive the open/closed Picard-Fuchs differential equations, which control…
Doran and Morgan have introduced certain rational basis for the monodromy group of the Picard-Fuchs operator of a hypergeometric family of Calabi-Yau threefolds. In this paper we compute numerically the transition matrix between a…
We study Calabi-Yau manifolds defined over finite fields. These manifolds have parameters, which now also take values in the field and we compute the number of rational points of the manifold as a function of the parameters. The intriguing…
We prove that certain differential operators of the form $DLD$ with $L$ hypergeometric and $D=z \frac{d}{dz}$ are of Picard-Fuchs type. We give closed hypergeometric expressions for minors of the biextension period matrices that arise from…