Related papers: Hesse Pencils and 3-Torsion Structures
In this paper we analyse the structure of the spaces of smooth type functions, generated by elements of arbitrary Hilbert spaces, as a continuation of the research in our previous papers in this series. We prove that these spaces are…
In this paper we develop methods to extend the minimal hypersurface approach to positive scalar curvature problems to all dimensions. This includes a proof of the positive mass theorem in all dimensions without a spin assumption. It also…
In this paper we consider a random partition of the plane into cells, the partition being based on the nodes and links of a {\it random planar geometric graph}. The resulting structure generalises the \emph{random \tes}\ hitherto studied in…
This paper is devoted to a discussion of specific properties of invariants in the theory of forms.
The purpose of this paper is to investigate forcing as a tool to construct universal models. In particular, we look at theories of initial segments of the universe and show that any model of a sufficiently rich fragment of those theories…
We give a formula for the Euler characteristic of a triangulated manifold of even dimension in terms of the numbers of even-dimensional faces only. The coefficients in this formula are universal (they do not depend on the dimension of the…
We study Ramsey expansions of certain homogeneous 3-hypertournaments. We show that they exhibit an interesting behaviour and, in one case, they seem not to submit to current gold-standard methods for obtaining Ramsey expansions. This makes…
The three pencils of K3 surfaces of minimal discriminant whose general element covers at least one Enriques surface are Kond\={o}'s pencils I and II, and the Ap\'ery--Fermi pencil. We enumerate and investigate all Enriques surfaces covered…
The purpose of this paper is twofold; (1) to develop several identities for the Generalized $k$-Pell sequence (including those of Binet, Catalan, Cassini, and d'Ocagne), and (2) to study applications of tridiagonal generating matrices for…
Given an $L^2$-acyclic connected finite $CW$-complex, we define its universal $L^2$-torsion in terms of the chain complex of its universal covering. It takes values in the weak Whitehead group $\operatorname{Wh}^w(G)$. We study its main…
The properties of the spaces of Sugeno integrable functions are quite different from those of the ordinary spaces of Lebesgue integrable functions. The purpose of the paper is to further advance our study of the Sugeno-Lorentz spaces, in…
Even if there are too many elliptic fibrations to investigate and describe on the singular $K3$ surface $Y_{10}$ of discriminant 72 and belonging to the Ap\'ery-Fermi pencil $(Y_k)$, we find on it many interesting properties. For example…
We give the addition formula for the tropical Hesse pencil, which is the tropicalization of the Hesse pencil parametrized by the level-three theta functions, via those for the ultradiscrete theta functions. The ultradiscrete theta functions…
The blown up complex projective plane in the twelve triple points of the dual Hesse arrangement has an infinite number of irreducible rational curves of self-intersection $-1$, for short, $(-1)$-curves. In the preprint version of [Dumnicki,…
Consider three normalised cuspidal eigenforms of weight $2$ and prime level $p$. Under the assumption that the global root number of the associated triple product $L$-function is $+1$, we prove that the complex Abel-Jacobi image of the…
The aim of this paper is state of conditions that ensure the convexity of a Chebyshev sets in Hilbert spaces .
In this paper we are interested in non trivial bi-Hamiltonian deformations of the Poisson pencil $\omega_{\lambda}=\omega_2+\lambda \omega_1=u\delta'(x-y)+\f{1}{2}u_x\delta(x-y)+\lambda\delta'(x-y)$. Deformations are generated by a sequence…
We rewrite the property of confocality with respect to a pseudo-Euclidean space. Our observation is that the generalized definition of confocality in $\cite{stachel}$ does not give back to the original definition of confocality of Euclidean…
A set of new tensors of purely geometric origin have been investigated, which form a hierarchy. A tensor of a lower rank plays the role of the potential for the tensor of one rank higher. The tensors have interesting mathematical and…
For a tensor product of algebras twisted by a bicharacter, we completely describe its Hochschild cohomology, as a Gerstenhaber algebra, in terms of the Hochschild cohomology of its component parts. This description generalizes a result of…