首页/论文/2005.08181

arXiv 2005.081812020-05math.AGmath.CO

Configuration polynomials under contact equivalence

Graham Denham, Delphine Pol, Mathias Schulze, Uli Walther

备注：: 19 pages, 1 table
DOI：: 10.4171/AIHPD/154

英文摘要：

Configuration polynomials generalize the classical Kirchhoff polynomial defined by a graph. Their study sheds light on certain polynomials appearing in Feynman integrands. Contact equivalence provides a way to study the associated configuration hypersurface. In the contact equivalence class of any configuration polynomial we identify a polynomial with minimal number of variables; it is a configuration polynomial. This minimal number is bounded by $r+1\choose 2$, where $r$ is the rank of the underlying matroid. We show that the number of equivalence classes is finite exactly up to rank $3$ and list explicit normal forms for these classes.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Blow-Analytic Equivalence versus contact-bi-Lipschitz Equivalence

Two blow-analytically equivalent real analytic plane function germs are sub-analytically bi-Lipschitz contact equivalent

2016-01-25math.AGmath.MG

Invariants of the bi-Lipschitz contact equivalence of continuous definable function germs

We construct an invariant of the bi-Lipschitz contact equivalence of continuous function germs definable in a polynomially bounded o-minimal structure, such as semialgebraic functions. For a germ $f,$ the invariant is given in terms of the leading coefficients of the asymptotic expansions of $f$ along the connected components of the tangency variety of $f.$

2019-01-14math.AG

Lipschitz contact equivalence of function germs in $\mathbb{R}^2$

In this paper we study Lipschitz contact equivalence of continuous function germs in the plane definable in a polynomially bounded o-minimal structure, such as semialgebraic and subanalytic functions. We partition the germ of the plane at the origin into zones where the function has explicit asymptotic behavior. Such a partition is called a pizza. We show that each function germ admits a minimal pizza, unique up to combinatorial equivalence. We show then that two definable continuous function germs are definably Lipschitz contact equivalent if and only if their corresponding minimal pizzas are…

2014-07-10math.AG

Invariants of Relative Right and Contact Equivalences

We study holomorphic function germs under equivalence relations that preserve an analytic variety. We show that two quasihomogeneous polynomials, not necessarily with isolated singularities, having isomorphic relative Milnor algebras are relative right equivalent. Under the condition that the module of vector fields tangent to the variety is finitely generated, we also show that the relative Tjurina algebra is a complete invariant for the classification of arbitrary function germs with respect to the relative contact equivalence. This is the relative version of a well known result by Mather an…

2019-04-06math.AG

On the bi-Lipschitz contact equivalence of plane complex function-germs

In this short note, we consider the problem of bi-Lipschitz contact equivalence of complex analytic function-germs of two variables. It is inquiring about the infinitesimal sizes of such function-germs, up to bi-Lipschitz changes of coordinates. We show that this problem is equivalent to the problem of the right topological classification.

2014-01-22math.AG

高阶雅可比理想、接触等价与动机zeta函数

Higher Jacobian ideals, contact equivalence and motivic zeta functions

本文研究高阶雅可比理想的性质，证明高阶Nash blowing-up代数在接触等价下不变，并得到动机近旁循环结果的类比，从而推进了函数奇点的研究。

2023-10-12math.ACmath.AG

更多相关论文收起更多论文

$Γ-Σ-C^{0}-$determinacy of $Γ-Σ-C^{0}-$equivariant bifurcation problems with respect to $Γ-Σ-C^{0}-$BD and contact equivalence from the weighted point view

In this paper, $C^{0}$ finite determination of $Γ-$equivariant bifurcation problems in the relative case from the weighted point view is being discussed . Some criteria on the $C^{0}$ finite determination of $Γ-$equi-variant bifurcation problems in the relative case are then obtained in terms of an analytic-geometric non-degeneracy condition, which generalize the result on the $C^{0}$ finite determination of bifurcation problems given by P.B.Percell and P.N.Brown.

2021-08-28math.AG

Equivalence of symplectic singularities

Let X be an affine normal variety with a C^*-action having only positive weights. Assume that X_{reg} has a symplectic 2-form w of weight l. We prove that, when l is not zero, the w is a unique symplectic 2-form of weight l up to C^*-equivariant automorphism When $l = 0$, we have a counter-example to this statement. In the latter half of the article, we associate to X a projective variety P(X) and prove that P(X) has a contact orbifold structure. Moreover, when X has canonical singularities, the contact orbifold structure is rigid under a small deformation. By using the contact structure on P(…

2013-04-05math.AG

Moduli spaces of semiquasihomogeneous singularities with fixed principal part

We construct coarse moduli spaces of semiquasihomogeneous hypersurface singularities with respect to right equivalence and contact equivalence. We have to fix the principal part of the semiquasihomogeneous singularities. For the moduli spaces with respect to contact equivalence we also fix the Hilbert function of the Tjurina algebra induced by the weights.

1995-03-22alg-geommath.AG

Normal Forms of Hypersurface Singularities in Positive Characteristic

The main purpose of this article is to lay the foundations for a classification of isolated hypersurface singularities in positive characteristic. Although our article is in the spirit of Arnol'd who classified real an complex hypersurfaces in the 1970's with respect to right equivalence, several new phenomena occur in positive characteristic. Already the notion of isolated singularity is different for right resp. contact equivalence over fields of characteristic other than zero. The heart of this paper consists of the study of different notions of non-degeneracy and the associated piecewise f…

2010-11-17math.ACmath.AG

Rational normal curves and Hadamard products

Given $r>n$ general hyperplanes in $\mathbb P^n,$ a star configuration of points is the set of all the $n$-wise intersection of them. We introduce {\it contact star configurations}, which are star configurations where all the hyperplanes are osculating to the same rational normal curve. In this paper we find a relation between this construction and Hadamard products of linear varieties. Moreover, we study the union of contact star configurations on a same conic in $\mathbb P^2$, we prove that the union of two contact star configurations has a special $h$-vector and, in some cases, this is a co…

2021-02-09math.ACmath.AG