Results 81 to 90 of about 1,716 (199)

Bimonoids for hyperplane arrangements

, 2020
Develops a new theory, parallel to the classical theory of connected Hopf algebras, including a real hyperplane ...
Aguiar, Marcelo, Mahajan, Swapneel
core  

The broken circuit complex and the Orlik - Terao algebra of a hyperplane arrangement [PDF]

, 2016
My thesis is mostly concerned with algebraic and combinatorial aspects of the theory of hyperplane arrangements. More specifically, I study the Orlik-Terao algebra of a hyperplane arrangement and the broken circuit complex of a matroid.
Le, Van Dinh
core  

A Miyaoka–Yau inequality for hyperplane arrangements in CPn$\mathbb {CP}^n$

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract Let H$\mathcal {H}$ be a hyperplane arrangement in CPn$\mathbb {CP}^n$. We define a quadratic form Q$Q$ on RH$\mathbb {R}^{\mathcal {H}}$ that is entirely determined by the intersection poset of H$\mathcal {H}$. Using the Bogomolov–Gieseker inequality for parabolic bundles, we show that if a∈RH$\mathbf {a}\in \mathbb {R}^{\mathcal {H}}$ is ...
Martin de Borbon, Dmitri Panov
wiley   +1 more source

k-Adjoint of hyperplane arrangements

Journal of Combinatorial Theory, Series A
In this paper, we introduce the $k$-adjoint of a given hyperplane arrangement $\mathcal{A}$ associated with rank-$k$ elements in the intersection lattice $L(\mathcal{A})$, which generalizes the classical adjoint proposed by Bixby and Coullard. The $k$-adjoint of $\mathcal{A}$ induces a decomposition of the Grassmannian, which we call the $\mathcal{A ...
Weikang Liang, Suijie Wang, Chengdong Zhao   +2 more
openaire   +2 more sources

A note on kinematic flow and differential equations for two-site one-loop graph in FRW spacetime

Journal of High Energy Physics
In this work, we systematically study the differential systems governing loop-level wavefunction coefficients of conformally-coupled scalar field theory within a general power-law FRW cosmology.
Yanfeng Hang, Cong Shen
doaj   +1 more source

Perverse Sheaves and Hyperplane Arrangements

, 2017
The category of Perverse Sheaves is known to be an Abelian and Artinian category. As a result, we can talk about the length and decomposition factors of a perverse sheaf. In this thesis we look at a class of perverse sheaves arising from local systems on
Luis Ernesto Saumell (17554713)
core   +1 more source

Tate properties, polynomial-count varieties, and monodromy of hyperplane arrangements

, 2012
In this new version some references are added for Thom-Sebastiani type results for the productof two functions. Note that all the previous results make no claim on the corresponding mixed Hodge structures, which is a key point in our paperInternational ...
Dimca, Alexandru
core   +2 more sources

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

The face semigroup algebra of a hyperplane arrangement

, 2005
The first part of this thesis studies the face semigroup algebra of a hyperplane arrangement. The quiver with relations of the algebra is computed and the algebra is shown to be a Koszul algebra.
Franco Valentino Saliola, Franco V Saliola   +1 more
core  

Odd Khovanov homology for hyperplane arrangements

, 2016
We define several homology theories for central hyperplane arrangements, categorifying well-known polynomial invariants including the characteristic polynomial, Poincaré polynomial, and Tutte polynomial.
Dancso, Zsuzsanna, Licata, Anthony
core   +1 more source