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of 572
pro vyhledávání: '"32s22"'
Autor:
Bromboszcz, Artur
In this note we focus on combinatorial aspects of plus-one generated line arrangements. We provide combinatorial constraints on such arrangements and we present new examples of plus-one generated arrangements constructed by using classical Klein and
Externí odkaz:
http://arxiv.org/abs/2411.17317
Autor:
Shi, Quan, Zuo, Huaiqing
Suppose $f = f_1^{b_1}...f_r^{b_r}\in \mathbb C[z_1,...,z_n]\setminus \mathbb C$. We introduce a variation of archimedean zeta function about $f_1,...,f_r$ and give a condition for generic existence of a type of poles. As an application, in the case
Externí odkaz:
http://arxiv.org/abs/2411.00757
We define the type of a plane curve as the initial degree of the corresponding Bourbaki ideal. Then we show that this invariant behaves well with respect to the union of curves. The curves of type $0$ are precisely the free curves and the curves of t
Externí odkaz:
http://arxiv.org/abs/2410.11479
Autor:
Okura, Takuma
In Terao [24], Hiroaki Terao defined and studied "admissible map", which is a generalization of "social welfare function" in the context of hyperplane arrangements. Using this, he proved a generalized Arrow's Impossibility Theorem using combinatorial
Externí odkaz:
http://arxiv.org/abs/2408.14263
The goal of this paper is to establish a new characterization of quasi-homogeneous isolated singularities of free curves and nearly free curves $C$ in $\mathbb{P}_\mathbb{C}^2$. The criterion will be in terms of a first syzygy matrix associated with
Externí odkaz:
http://arxiv.org/abs/2407.05819
Cuntz and K\"uhne introduced the class of connected subgraph arrangements $A_G$, depending on a graph $G$, and classified all graphs $G$ such that the corresponding arrangement $A_G$ is free. We extend their result to the multiarrangement case and cl
Externí odkaz:
http://arxiv.org/abs/2406.19866
Autor:
Abe, Takuro, Kawanoue, Hiraku
There are two restriction maps of the logarithmic modules of plane arrangements in a three dimensional vector space. One is the Euler restriction and the other is the Ziegler restriction. The dimension of the cokernel of the Ziegler restriction map o
Externí odkaz:
http://arxiv.org/abs/2406.00305
Characteristic quasi-polynomials are the enumerative functions counting the number of elements in the complement of hyperplane arrangements modulo positive integers.In this paper, we compute the characteristic quasi-polynomials of the restriction of
Externí odkaz:
http://arxiv.org/abs/2405.20102
Autor:
Horiguchi, Tatsuya
Regular nilpotent Hessenberg varieties are subvarieties of full flag varieties, while regular nilpotent partial Hessenberg varieties are subvarieties of partial flag varieties. In this manuscript we first provide a summand formula and a product formu
Externí odkaz:
http://arxiv.org/abs/2405.07247
Autor:
Bath, Daniel, Walther, Uli
Given a matroid or flag of matroids we introduce several broad classes of polynomials satisfying Deletion-Contraction identities, and study their singularities. There are three main families of polynomials captured by our approach: matroidal polynomi
Externí odkaz:
http://arxiv.org/abs/2404.07885