相关论文: Eisenstein type series for Calabi-Yau varieties
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 use the Gromov-Witten/Pairs descendent correspondence for toric 3-folds and degeneration arguments to establish the GW/P correspondence for several compact Calabi-Yau 3-folds (including all CY complete intersections in products of…
In this paper we construct Mabuchi $\mathcal{L}^{{\rm M}}_{\omega}$ functional and Aubin-Yau functionals $\mathcal{I}^{{\rm AY}}_{\omega}, \mathcal{J}^{{\rm AY}}_{\omega}$ on any compact complex three-folds. The method presented here will…
In the present paper we propose a combinatorial approach to study the so called double octic Clabi--Yau threefolds. We use this description to give a complete classification of double octics with $h^{1,2}\le1$ and to derive their geometric…
We investigate the structures of Calabi-Yau differential equations and the relations to the arithmetic of the pencils of Calabi-Yau varieties behind the equations. This provides explanations of some observations and computations in a recent…
We present an exhaustive, constructive, classification of the Calabi-Yau four-folds which can be described as complete intersections in products of projective spaces. A comprehensive list of 921,497 configuration matrices which represent…
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…
In this talk we discuss the construction of a basis of master integrals for the family of the $l$-loop equal-mass banana integrals, such that the differential equation is in an $\varepsilon$-factorised form. As the $l$-loop banana integral…
We study modular differential equations for the basic weak Jacobi forms in one abelian variable with applications to the elliptic genus of Calabi--Yau varieties. We show that the elliptic genus of any $CY_3$ satisfies a differential…
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.
Using deformed or twisted Eisenstein Series, we construct a Jacobi-Serre derivative on even-weight Jacobi forms that generalizes the classical Serre derivative on modular forms. As an application, we obtain Ramanujan equations for the index…
A complete analysis of all heterotic Calabi-Yau compactifications based on positive two-term monad bundles over favourable complete intersection Calabi-Yau threefolds is performed. We show that the original data set of about 7000 models…
In this paper, the numbers of rational curves on general complete intersection Calabi-Yau threefolds in complex projective spaces are computed up to degree six. The results are all in agreement with the predictions made from mirror…
This note studies the equivalencies among convergences of Ricci-flat K\"{a}hler-Einstein metrics on Calabi-Yau manifolds, cohomology classes and potential functions.
In this short note we construct Calabi-Yau threefolds with nonabelian fundamental groups of order 64 as quotients of the small resolutions of certain complete intersections of quadrics in $\PP^7$ that were first considered by M. Gross and…
We present a list of arithmetically Gorenstein Calabi-Yau threefolds in $\mathbb{P}^7$ and give evidence that this is a complete list. In particular we construct three new families of arithmetically Gorenstein Calabi-Yau threefolds in…
We introduce a special class of convex rational polyhedral cones which allows to construct generalized Calabi-Yau varieties of dimension $(d + 2(r-1))$, where $r$ is a positive integer and d is the dimension of critical string vacua with…
Certain Feynman integrals are associated to Calabi-Yau geometries. We demonstrate how these integrals can be computed with the method of differential equations. The four-loop equal-mass banana integral is the simplest Feynman integral whose…
We study the Poincare polynomials of all known Calabi-Yau three-folds as constrained polynomials of Littlewood type, thus generalising the well-known investigation into the distribution of the Euler characteristic and Hodge numbers. We find…
We show how the smooth geometry of Calabi-Yau manifolds emerges from the thermodynamic limit of the statistical mechanical model of crystal melting defined in our previous paper arXiv:0811.2801. In particular, the thermodynamic partition…