Related papers: Universally defined cycles I

We introduce the notion of families of n-marked smooth rational tropical curves over smooth tropical varieties and establish a one-to-one correspondence between (equivalence classes of) these families and morphisms from smooth tropical…

We prove a moving lemma for the additive and ordinary higher Chow groups of relative $0$-cycles of regular semi-local $k$-schemes essentially of finite type over an infinite perfect field. From this, we show that the cycle classes can be…

Many polynomial invariants are defined on graphs for encoding the combinatorial information and researching them algebraically. In this paper, we introduce the cycle polynomial and the path polynomial of directed graphs for counting cycles…

In this paper we discuss the notion of universality for classes of candidate common Lyapunov functions of linear switched systems. On the one hand, we prove that a family of absolutely homogeneous functions is universal as soon as it…

We study semantic and syntactic properties of spherical orders and their elementary theories, including finite and dense orders and their theories. It is shown that theories of dense $n$-spherical orders are countably categorical and…

Let $X$ be a smooth variety over a finite field $\mathbb{F}_q$. Let $\ell$ be a rational prime number invertible in $\mathbb{F}_q$. For an $\ell$-adic sheaf $\mathcal{F}$ on $X$, we construct a cycle supported on the singular support of…

The purpose of this work is to establish a link between the theory of Chern classes for singular varieties and the geometry of the varieties in question. Namely, we show that if $Z$ is a hypersurface in a compact complex manifold, defined…

Using determinantal schemes, we construct explicit cycles in the higher Chow complex of BGL that represent the universal Chern classes in higher Chow groups. As an application, we use these cycles, along with a canonical \emph{stable moving…

Given a reduced analytic space $Y$ we introduce a class of {\it nice} cycles, including all effective $\mathbb{Q}$-Cartier divisors. Equidimensional nice cycles that intersect properly allow for a natural intersection product. Using…

We establish closed-form expansions for the universal edge elimination polynomial of paths and cycles and their generating functions. This includes closed-form expansions for the bivariate matching polynomial, the bivariate chromatic…

We prove smoothness in the dg sense of the bounded derived category of finitely generated modules over any finite-dimensional algebra over a perfect field, hereby answering a question of Iyama. More generally, we prove this statement for…

Let $C_{m}$ be a cycle with length $m.$ The $k$-uniform hypercycle with length $m$ obtained by adding $k-2$ new vertices in every edge of $C_{m},$ denoted by $C_{m,k}.$ In this paper, we obtain some trace formulas of uniform hypercycles…

Universal cycles are generalizations of de Bruijn cycles and Gray codes that were introduced originally by Chung, Diaconis, and Graham in 1992. They have been developed by many authors since, for various combinatorial objects such as…

In this article, we apply some ideas developped by M. Cha{\l}upnik to the framework of strict polynomial bifunctors. This allows us to get a new proof of the existence of the `universal classes' originally constructed by the author.

A general framework for the reduction of the equations defining classes of spherical varieties to (maybe infinite dimensional) grassmannians is proposed. This is applied to model varieties of type A, B and C; in particular a standard…

Taking symmetric powers of varieties can be seen as a functor from the category of varieties to the category of varieties with an action by the symmetric group. We study a corresponding map between the Grothendieck groups of these…

We study the effective cones of cycles on universal hypersurfaces on a projective variety $X$, particularly focusing on the case of universal hypersurfaces in $\mathbb{P}^n$. We determine the effective cones of cycles on the universal conic…

By introducing a notion of smooth connection for unbounded $KK$-cycles, we show that the Kasparov product of such cycles can be defined directly, by an algebraic formula. In order to achieve this it is necessary to develop a framework of…

We discuss algebraic universality in the sense of P. Vogel for the simplest refined quantity, the Macdonald dimensions. The main known source of universal quantities is given by Chern-Simons theory. Refinement of Chern-Simons theory means…

Universal cycle for $k$-permutations is a cyclic arrangement in which each $k$-permutation appears exactly once as $k$ consecutive elements. Enumeration problem of universal cycles for $k$-permutations is discussed and one new enumerating…