Related papers: Orphan Calabi-Yau threefold with arithmetic monodr…

We show that for any smooth Calabi-Yau threefold $X$ of Picard number $2$ with infinite birational automorphism group, the numerical dimension $\kappa_\sigma$ of the extremal rays of the movable cone of $X$ is $\frac{3}{2}$. Furthermore, we…

A numerical algorithm for explicitly computing the spectrum of the Laplace-Beltrami operator on Calabi-Yau threefolds is presented. The requisite Ricci-flat metrics are calculated using a method introduced in previous papers. To illustrate…

The global behaviour of the normal function associated with van Geemen's family of lines on the mirror quintic is studied. Based on the associated inhomogeneous Picard-Fuchs equation, the series expansions around large complex structure,…

Let $p$ be an idempotent ultrafilter over $\mathbb{N}$. For a positive integer $N$, let ${\cal P}_{\leq N}$ denote the additive group of polynomials $P\in\mathbb{Z}[x]$ with ${\rm deg}\, P\leq N$ and $P(0)=0$. Given a unitary operator $U$…

The title is self-explanatory.

Assume that the local universal deformation of a Calabi-Yau 3-manifold X has an automorphism which does not act by 1 or -1 on the third cohomology. We show that the $F^2$ bundle in the Variation of Hodge structures of each maximal family…

This is the first of a series of papers devoted to the topology of symplectic Calabi-Yau $4$-manifolds endowed with certain symplectic finite group actions. We completely determine the fixed-point set structure of a finite cyclic action on…

We provide an explicit construction for a complete set of orthogonal primitive idempotents of finite group algebras over nilpotent groups. Furthermore, we give a complete set of matrix units in each simple epimorphic image of a finite group…

We describe how to find period integrals and Picard-Fuchs differential equations for certain one-parameter families of Calabi-Yau manifolds. These families can be seen as varieties over a finite field, in which case we show in an explicit…

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 mirror symmetry in Calabi-Yau manifolds M, three point functions of A(M)-model operators on the genus $0$ Riemann surface in cases of one-parameter families of $d$-folds realized as Fermat type hypersurfaces embedded in weighted…

Previously we constructed Calabi-Yau threefolds by a differential-geometric gluing method using Fano threefolds with their smooth anticanonical $K3$ divisors (New York J. Math. 20: 1-33, 2014). In this paper, we further consider the…

We present new computational results for symplectic monodromy groups of hypergeometric differential equations. In particular, we compute the arithmetic closure of each group, sometimes justifying arithmeticity. The results are obtained by…

We consider a large family of dynamical Belyi maps of arbitrary degree and study the arithmetic monodromy groups attached to the iterates of such maps. Building on the results of Bouw-Ejder-Karemaker on the geometric monodromy groups of…

We study in detail the profinite group G arising as geometric \'etale iterated monodromy group of an arbitrary quadratic polynomial over a field of characteristic different from two. This is a self-similar closed subgroup of the group of…

We develop classes of one-parameter families (OPF) of operators on $C^\infty_c(\mathbb{C})$ which characterize the behavior of operators associated to the $\bar\partial$-problem in $L^2(\mathbb{C},e^{-2p})$ where $p$ is a subharmonic,…

Using the Gelfand-Kapranov-Zelevinsk\u{\i} system for the primitive cohomology of an infinite series of complete intersection Calabi-Yau manifolds, whose dimension is the loop order minus one, we completely clarify the analytic structure of…

We study the Zariski closure of the monodromy group $\mathbf{Mon}$ of Lauricella's hypergeometric function $F_C$. If the identity component $\mathbf{Mon}^0$ acts irreducibly, then $\overline{\mathbf{Mon}} \cap \mathbf{SL}_{2^n}(\mathbb{C})$…

We show that Nichols algebras of most simple Yetter-Drinfeld modules over the projective symplectic linear group over a finite field, corresponding to unipotent orbits, have infinite dimension. We give a criterium to deal with unipotent…

In a series of papers \cite{KS,MR}, Krawitz, Milanov, Ruan, and Shen have verified the so-called Landau-Ginzburg/Calabi-Yau (LG/CY) correspondence for simple elliptic singularities $E_N^{(1,1)}$ ($N=6,7,8$). As a byproduct it was also…