Related papers: A Note on Schoen's Calabi--Yau Threefolds

Motivated by S-duality modularity conjectures in string theory, we define new invariants counting a restricted class of 2-dimensional torsion sheaves, enumerating pairs $Z\subset H$ in a Calabi-Yau threefold X. Here H is a member of a…

We discuss two closely related Calabi-Yau theorems for degenerations of compact K\"ahler manifolds. The first is a Calabi-Yau theorem for big test configurations, that generalizes a result in [WN24]. It follows from recent joint work with…

We study the Drinfeld double of the (equivariant spherical) Cohomological Hall algebra in the sense of Kontsevich and Soibelman, associated to a smooth toric Calabi-Yau 3-fold $X$. By general reasons, the COHA acts on the cohomology of the…

We formulate a generalization of Givental-Kim's quantum hyperplane principle. This is applied to compute the quantum cohomology of a Calabi-Yau 3-fold defined as the rank 4 locus of a general skew-symmetric 7x7 matrix with coeffisients in…

We formulate the "real integral Hodge conjecture", a version of the integral Hodge conjecture for real varieties, and raise the question of its validity for cycles of dimension 1 on uniruled and Calabi-Yau threefolds and on rationally…

We attempt to define a new invariant I of (almost) Calabi-Yau 3-folds M, by counting special Lagrangian rational homology 3-spheres N in M in each 3-homology class, with a certain weight w(N) depending on the topology of N. This is…

In this note, we consider crepant resolutions of the quotient varieties of smooth quintic threefolds by Gorenstein group actions. We compute their Hodge numbers via McKay correspondence. In this way, we find some new pairs…

In this paper we discuss recent progress on the modularity of Calabi-Yau varieties. We focus mostly on the case of surfaces and threefolds. We will also discuss some progress on the structure of the L-function in connection with mirror…

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…

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…

Through classical modularity conjectures, the period integrals of a holomorphic $3$-form on a rigid Calabi-Yau threefold are interesting from the perspective of number theory. Although the (approximate) values of these integrals would be…

We propose a way to examine N=1 and N=2 string dualities on Calabi-Yau three-folds or extensions. Our way is to find out or to construct two types of toric representations of a Calabi-Yau three-fold, which contain phases topologically…

We use tropical curves and toric degeneration techniques to construct closed embedded Lagrangian rational homology spheres in a lot of Calabi-Yau threefolds. We apply this construction to the tropical curves obtained from the 2875 lines on…

The aim of the paper is to investigate the only two families $\mathcal{F}^A_{G}$ of Calabi-Yau $3$-folds $A/G$ with $A$ an abelian $3$-fold and $G\le \text{Aut}(A)$ a finite group acting freely: one in constructed by Catanese and Demleitner…

Studying the mirror symmetry of a Calabi-Yau threefold $X$ of the Reye congruence in $\mP^4$, we conjecture that $X$ has a non-trivial Fourier-Mukai partner $Y$. We construct $Y$ as the double cover of a determinantal quintic in $\mP^4$…

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 prove the modularity of Maschke's octic and two Calabi-Yau threefolds derived from it as double octic and quotient thereof by the Heisenberg group, as conjectured by Bini and van Geemen. The proofs rely on automorphisms of the varieties…

In the following we describe some examples of Calabi-Yau manifolds, which arise as desingularizations of certain Siegel threefolds. The first Siegel modular variety with a Calabi-Yau model and the essentially only one up to now has been…

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 provide the first explicit example of Type IIB string theory compactification on a globally defined Calabi-Yau threefold with torsion which results in a four-dimensional effective theory with a non-Abelian discrete gauge symmetry. Our…