Related papers: On the construction problem for Hodge numbers

Let $m,n,s,k$ be four integers such that $3\leq s \leq n$, $3\leq k\leq m$ and $ms=nk$. Set $d=\gcd(s,k)$. In this paper we show how one can construct a Heffter array $H(m,n;s,k)$ starting from a square Heffter array $H(nk/d;d)$ whose…

The symmetric Macdonald polynomials are able to be constructed out of the non-symmetric Macdonald polynomials. This allows us to develop the theory of the symmetric Macdonald polynomials by first developing the theory of their non-symmetric…

We give a way of constructing real variations of mixed Hodge structures over compact K\"ahler manifolds by using mixed Hodge structures on Sullivan's $1$-minimal models of certain differential graded algebras associated with real variations…

We study a pair of Calabi-Yau threefolds X and M, fibered in non-principally polarized Abelian surfaces and their duals, and an equivalence D^b(X) = D^b(M), building on work of Gross, Popescu, Bak, and Schnell. Over the complex numbers, X…

When $k<n$, we study the coherent systems that come from a BGN extension in which the quotient bundle is strictly semistable. In this case we describe a stratification of the moduli space of coherent systems. We also describe the strata as…

Let p and q be distinct odd primes and assume k is an algebraically closed field of characteristic zero. We classify all quasitriangular Hopf algebras of dimension pq^2 over k, which are not simple as Hopf algebras. Moreover, we obtained…

Theorem. Let M be a compact, connected, oriented smooth Riemannian n-manifold with non-empty boundary. Then the cohomology of the complex (Harm*(M),d) of harmonic forms on M is given by the direct sum H^p(Harm*(M),d) = H^p(M;R) +…

We consider the rooted trees which not have isomorphic representation and introduce a conception of complexity a natural number also. The connection between quantity such trees with $n$ edges and a complexity of natural number $n$ is…

The transcendental Hodge lattice of a projective manifold $M$ is the smallest Hodge substructure in $p$-th cohomology which contains all holomorphic $p$-forms. We prove that the direct sum of all transcendental Hodge lattices has a natural…

We consider the complex analogues of symmetric power moments of cubic exponential sums. These are symmetric powers of the classical Airy differential equation. We show that their de Rham cohomologies underlie an arithmetic Hodge structure…

Let V be the pseudo-Euclidean vector space of signature (p,q), p>2 and W a module over the even Clifford algebra Cl^0 (V). A homogeneous quaternionic manifold (M,Q) is constructed for any spin(V)-equivariant linear map \Pi : \wedge^2 W \to…

We give a complex polarized variation of Hodge structure over a compact K"ahler manifold $M$ which controls all finite-dimensional complex polarized variations of Hodge structure over $M$ and their tensor relations. As a corollary, we…

We show the classical $q$-Stirling numbers of the second kind can be expressed compactly as a pair of statistics on a subset of restricted growth words. The resulting expressions are polynomials in $q$ and $1+q$. We extend this enumerative…

There is considered the problem of describing up to linear conformal equivalence those harmonic cubic homogeneous polynomials for which the squared-norm of the Hessian is a nonzero multiple of the quadratic form defining the Euclidean…

Classical variational Hodge structure theory characterizes the algebraicity of Hodge classes by studying the transversality of period mappings under geometric deformations. However, when algebraic varieties lack appropriate deformation…

The Hirzebruch signature formula provides an obstruction to the following realization question: given a rational Poincar\'e duality algebra $\mathcal{A}$, does there exist a smooth manifold $M$ such that $H^*(M;\mathbb{Q})=\mathcal{A}$?…

Let $Y$ be a projective submanifold of the total space of the inverse of a very ample line bundle $\pi:L^{-1}\rightarrow B$ over a projective manifold $B$. Any section of $L^{-1}\rightarrow B$ is isomorphic to $B$ and the Hodge numbers of…

We introduce and study Hodge-de Rham numbers for compact almost complex 4-manifolds, generalizing the Hodge numbers of a complex surface. The main properties of these numbers in the case of complex surfaces are extended to this more general…

A compact symplectic manifold $(M, \omega)$ is said to satisfy the hard-Lefschetz condition if it is possible to develop an analogue of Hodge theory for $(M, \omega)$. This loosely means that there is a notion of harmonicity of differential…

In this paper we contribute to the classification of Hopf algebras of dimension pq, where p,q are distinct prime numbers. More precisely, we prove that if p and q are odd primes with p<q<2p+3, then any complex Hopf algebra of dimension pq…