Related papers: The reciprocal complement of a surface
We study the congruence of bitangent lines of an irreducible surface in the 3-dimensional projective space in arbitrary characteristic, with special attention to quartic surfaces with rational double points and, in particular, Kummer…
Let $R\subseteq E$ be two Lie conformal algebras and $Q$ be a given complement of $R$ in $E$. Classifying complements problem asks for describing and classifying all complements of $R$ in $E$ up to an isomorphism. It is known that $E$ is…
The main result of the paper is a boundedness for $n$-complements on algebraic surfaces. In addition, applications of this theorem to a classification of log Del Pezzo surfaces and of birational contractions for 3-folds are formulated.
We characterize pairs (Q,d) consisting of a quiver Q and a dimension vector d, such that over a given algebraically closed field k there are infinitely many representations of Q of dimension vector d. We also present an application of this…
Let $(K,\nu)$ be an arbitrary-rank valued field, $R_\nu$ its valuation ring, $K(\alpha)/K$ a separable finite field extension generated over $K$ by a root of a monic irreducible polynomial $f\in R_\nu[X]$. We give necessary and sufficient…
Let $R$ be a Dedekind ring, $K$ its quotient field, and $L=K(\alpha)$ a finite field extension of $K$ defined by a monic irreducible polynomial $f(x)\in R[x]$. We give an easy version of Dedekind's criterion which computationally improves…
A residue formula which evaluates any correlation function of topological $SU_n$ Yang-Mills theory with arbitrary magnetic flux insertion in two dimensions are obtained. Deformations of the system by two form operators are investigated in…
The theory of self-reciprocal functions is applied to the study Mordell type integrals. We find two particular eigenfunctions of the double cosine Fourier transform and then use them to evaluate certain one- and two-dimensional Mordell type…
The ring R of real-exponent polynomials in n variables over any field has global dimension n+1 and flat dimension n. In particular, the residue field k = R/m of R modulo its maximal graded ideal m has flat dimension n via a Koszul-like…
In this paper, we define and prove basic properties of complement polyhedral product spaces, dual complexes and polyhedral product complexes. Then we compute the universal algebra of polyhedral product complexes under certain split…
For any ring we propose the construction of a cover which increases the finitistic dimension on one side and decreases the finitistic dimension to zero on the opposite side. This complements recent work of Cummings.
Infinitesimal bendings for classes of two-dimensional surfaces in $\mathbb{R}^3$ are investigated. The techniques used to construct the bending fields include reduction to solvability of Bers-Vekua type equations and systems of differential…
Let $\Aa_t$ be the directed quiver of type $\Aa$ with $t$ vertices. For each dimension vector $d$ there is a dense orbit in the corresponding representation space. The principal aim of this note is to use just rank conditions to define the…
In this paper we define the coarse (co)homology of the complement of a subspace in a metric space, generalizing the coarse (co)homology of Roe. We give a model space which encodes coarse geometric structure of the complement. We also…
We study the algebraic $K$-theory of rings of the form $R[x]/x^e$. We do this via trace methods and filtrations on topological Hochschild homology and related theories by quasisyntomic sheaves. We produce computations for $R$ a perfectoid…
The algebraic foundation of tropical polynomial algebra provides the framework for the geometric construction of the supplement and the reversal of tropical varieties, thereby inducing a duality of reduced tropical varieties; for classes of…
A Klein surface is a surface with a dianalytic structure. A double of a Klein surface $X$ is a Klein surface $Y$ such that there is a degree two morphism (of Klein surfaces) $Y\rightarrow X$. There are many doubles of a given Klein surface…
In this paper we extend the unramified class field theory for arithmetic surfaces of K. Kato and S. Saito to the relative case. Let X be a regular proper arithmetic surface and let Y be the support of divisor on X. Let CH_0(X,Y) denote the…
For a d-dimensional polyhedral complex P, the dimension of the space of piecewise polynomial functions (splines) on P of smoothness r and degree k is given, for k sufficiently large, by a polynomial f(P,r,k) of degree d. When d=2 and P is…
Various formulas for reciprocals of densely defined weighted composition operators in $L^2$-spaces as well as for their adjoints are provided. The relation between the reciprocal of a weighted composition operator and the product of the…