Results 1 to 10 of about 28 (28)

Triangular arrangements on the projective plane [PDF]

Épijournal de Géométrie Algébrique, 2023
In this work we study line arrangements consisting in lines passing through three non-aligned points. We call them triangular arrangements. We prove that any combinatorics of a triangular arrangement is always realized by a Roots-of-Unity-Arrangement ...
Simone Marchesi, Jean Vallès
doaj  

Supersolvable orders and inductively free arrangements

Open Mathematics, 2017
In this paper, we define the supersolvable order of hyperplanes in a supersolvable arrangement, and obtain a class of inductively free arrangements according to this order.
Gao Ruimei, Cui Xiupeng, Li Zhe
doaj   +1 more source

LOCAL SYSTEMS ON COMPLEMENTS OF ARRANGEMENTS OF SMOOTH, COMPLEX ALGEBRAIC HYPERSURFACES

Forum of Mathematics, Sigma, 2018
We consider smooth, complex quasiprojective varieties $U$ that admit a compactification with a boundary, which is an arrangement of smooth algebraic hypersurfaces. If the hypersurfaces intersect locally like hyperplanes,
GRAHAM DENHAM, ALEXANDER I. SUCIU
doaj   +1 more source

On the freeness of hypersurface arrangements consisting of hyperplanes and spheres

Open Mathematics, 2018
Let V be a smooth variety. A hypersurface arrangement 𝓜 in V is a union of smooth hypersurfaces, which locally looks like a union of hyperplanes. We say 𝓜 is free if all these local models can be chosen to be free hyperplane arrangements.
Gao Ruimei, Dai Qun, Li Zhe
doaj   +1 more source

Inductive Freeness of Ziegler’s Canonical Multiderivations for Reflection Arrangements

, 2017
MSC: 20F55; 51F15; 52C35; 14N20; 32S22; 51D20Research in Pairs 2017Let $A$ be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction $A''$ of $A$ to any hyperplane endowed with the natural multiplicity is then a free ...
Hoge, Torsten, Röhrle, Gerhard
core   +1 more source

Hyperplane Arrangements Satisfy (Un)Twisted Logarithmic Comparison Theorems, Applications to $\mathscr {D}_{X}$ -modules

Forum of Mathematics, Pi
For a reduced hyperplane arrangement, we prove the analytic Twisted Logarithmic Comparison Theorem, subject to mild combinatorial arithmetic conditions on the weights defining the twist.
Daniel Bath
doaj   +1 more source

Hodge theory of abelian covers of algebraic varieties

Forum of Mathematics, Sigma
Motivated by classical Alexander invariants of affine hypersurface complements, we endow certain finite dimensional quotients of the homology of abelian covers of complex algebraic varieties with a canonical and functorial mixed Hodge structure (MHS ...
Eva Elduque, Moisés Herradón Cueto
doaj   +1 more source

On the diffeomorphic type of the complement to a line arrangement in a projective plane

Open Mathematics, 2012
Bogomolov Fedor, Kulikov Viktor
doaj   +1 more source

Localization of Plus-One Generated Arrangements

Communications in Algebra, 2021
Michele Torielli, Elisa Palezzato
exaly  

Unexpected Curves in ℙ2, Line Arrangements, and Minimal Degree of Jacobian Relations

Journal of Commutative Algebra, 2023
Alexandru Dimca
exaly