Related papers: Eisenstein type series for Calabi-Yau varieties

We study zeta-functions for a one parameter family of quintic threefolds defined over finite fields and for their mirror manifolds and comment on their structure. The zeta-function for the quintic family involves factors that correspond to…

In this paper the elliptic genus for a general Calabi-Yau fourfold is derived. The recent work of Kawai calculating N=2 heterotic string one-loop threshold corrections with a Wilson line turned on is extended to a similar computation where…

This note is a report on the observation that some singular varieties admit Calabi--Yau coverings. As an application, we construct 18 new Calabi--Yau 3-folds with Picard number one that have some interesting properties.

We introduce a nine-parameter Heun-type differential equation and obtain three classes of its solutions as series of square integrable functions written in terms of the Jacobi polynomial. The expansion coefficients of the series satisfy…

In a recent paper, Doran, Greene and Judes considered one parameter families of quintic threefolds with finite symmetry groups. A surprising result was that each of these six families has the same Picard Fuchs equation associated to the…

In this paper, we prove the Kobayashi hyperbolicity of the coarse moduli spaces of canonically polarized or polarized Calabi-Yau manifolds in the sense of complex $V$-spaces (a generalization of complex $V$-manifolds in the sense of…

In this paper, we introduce the notion of parabolic stable pairs on Calabi-Yau 3-folds and invariants counting them. By applying the wall-crossing formula developed by Joyce-Song, Kontsevich-Soibelman, we see that they are related to…

In this paper, we will apply the ideas from the mirror symmetry of Calabi-Yau threefolds to study the modular forms and one-parameter family of K3 surfaces found by Beukers and Peters, which provide enlightenment to the two mysterious…

We give a differential-geometric construction of Calabi-Yau fourfolds by the `doubling' method, which was introduced in \cite{DY14} to construct Calabi-Yau threefolds. We also give examples of Calabi-Yau fourfolds from toric Fano fourfolds.…

We define and investigate deformed n-Calabi-Yau completions of homologically smooth differential graded (=dg) categories. Important examples are: deformed preprojective algebras of connected non Dynkin quivers, Ginzburg dg algebras…

We study Riemannian geometry of canonical Kahler-Einstein currents on projective Calabi-Yau varieties and canonical models of general type with crepant singularities. We prove that the metric completion of the regular part of such a…

An exact Calabi-Yau structure, originally introduced by Keller, is a special kind of smooth Calabi-Yau structure in the sense of Kontsevich-Vlassopoulos. For a Weinstein manifold $M$, the existence of an exact Calabi-Yau structure on the…

For a one parameter family of Calabi-Yau threefolds, Green, Griffiths and Kerr have expressed the total singularities in terms of the degrees of Hodge bundles and Euler number of the general fiber. In this paper, we show that the total…

We show that for any smooth Calabi--Yau variety, its index can be realized as the index of a Kawamata log terminal (klt) Calabi--Yau pair of lower dimension with standard coefficients. Our approach is based on an inductive argument on the…

We apply a universal normal Calabi-Yau algebra to the construction and classification of compact complex $n$-dimensional spaces with SU(n) holonomy and their fibrations. This algebraic approach includes natural extensions of reflexive…

We briefly review the formal picture in which a Calabi-Yau $n$-fold is the complex analogue of an oriented real $n$-manifold, and a Fano with a fixed smooth anticanonical divisor is the analogue of a manifold with boundary, motivating a…

We discuss Calabi-Yau and fractional Calabi-Yau semiorthogonal components of derived categories of coherent sheaves on smooth projective varieties. The main result is a general construction of a fractional Calabi-Yau category from a…

This paper describes the derivation of the level 5 versions of Ramanujan's system of ordinary differential equations satisfied by the Eisenstein series, $E_2(q),E_4(q)$, and $E_6(q).$

In this paper we are concerned with the monodromy of Picard-Fuch differential equations associated with one-parameter families of Calabi-Yau threefolds. Our results show that in the hypergeometric cases the matrix representations of…

The integrable systems associated with Seiberg-Witten geometry are considered both from the Hitchin-Donagi-Witten gauge model and in terms of intermediate Jacobians of Calabi-Yau threefolds. Dual pairs and enhancement of gauge symmetries…