Related papers: Tables of Calabi--Yau equations
Historically, the study of graded (twisted or otherwise) Calabi--Yau algebras has meant the study of such algebras under an $\mathbb{N}$-grading. In this paper, we propose a suitable definition for a twisted $G$-graded Calabi-Yau algebra,…
This paper contains a preliminary study of the monodromy of certain fourth order differential equations, that were called of Calabi-Yau type in math.NT/0402386. Some of these equations can be interpreted as the Picard-Fuchs equations of a…
We present here the solution of the problem on linearization of fourth-order equations by means of point transformations. We show that all fourth-order equations that are linearizable by point transformations are contained in the class of…
We study the solvability of a class of fully nonlinear equations on the flat torus. The equations arise in the study of some Calabi-Yau type problems in torus bundles.
We review briefly the characteristic topological data of Calabi--Yau threefolds and focus on the question of when two threefolds are equivalent through related topological data. This provides an interesting test case for machine learning…
In a previous study, we constructed a family of elliptic Calabi-Yau 4-folds possessing a geometric structure that allowed them to be split into a pair of rational elliptic 4-folds. In the present study, we introduce a method of classifying…
In this paper we prove the existence and uniqueness of the form-type Calabi-Yau equation on K\"ahler manifolds of nonnegative orthogonal bisectional curvature.
The aim of this note is to investigate characterizations and deformations of elliptic Calabi--Yau manifolds, building on earlier works of Wilson and Oguiso. Version 2: References updated and small changes. Version 3: Smoothness conditions…
We construct higher-dimensional Calabi-Yau varieties defined over a given number field with Zariski dense sets of rational points. We give two elementary constructions in arbitrary dimensions as well as another construction in dimension…
We construct several examples of higher-dimensional Calabi-Yau manifolds and prove their modularity.
In this essay we aim to explore the Geometric aspects of the Calabi Conjecture and highlight the techniques of nonlinear Elliptic PDE theory used by S.T. Yau [SY] in obtaining a solution to the problem. Yau proves the existence of a…
We classify, up to isomorphism, twisted graded Calabi--Yau algebras of dimension two on two-vertex quivers. By work of Reyes and Rogalski, such algebras may be presented as quotients of translation quivers by mesh relations. We also…
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
We prove that the Calabi-Yau equation can be solved on the Kodaira-Thurston manifold for all given $T^2$-invariant volume forms. This provides support for Donaldson's conjecture that Yau's theorem has an extension to symplectic…
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…
Let $X$ denote the total space of cotangent bundle of projective plane. This is a non-compact Calabi-Yau $4$-fold (also called local Calabi-Yau variety in physics literature). The aim of this paper is to use tilting objects to characterize…
A class of fourth--order neutral type difference equations with quasidifferences and deviating arguments is considered. Our approach is based on studying the considered equation as a system of a four--dimensional difference system. The…
It is well-known that any solution of the Laplace equation is a real or imaginary part of a complex holomorphic function. In this paper, in some sense, we extend this property into four order hyperbolic and elliptic type PDEs. To be more…
We generalise a method recently introduced in the literature, that derives canonical differential equations, to multi-scale Feynman integrals with an underlying Calabi-Yau geometry. We start by recomputing a canonical form for the sunrise…
Inspired Yau's work (Comm. Anal. Geom., 1994), in this short note we provide a new version of Li-Yau gradient estimate for the linear heat equation, which generalizes some known results and gives new gradient estimates. Also we explain the…