Related papers: Weyl and Zariski chambers on projective surfaces

We introduce and study a new class of representations of surface groups into Lie groups of Hermitian type, called {\em weakly maximal} representations. We prove that weakly maximal representations are discrete and injective and we describe…

The objective of this paper is to describe the structure of Zariski closed algebras, which provide a useful generalization to finite dimensional algebras in the study of representable algebras over finite fields. Our results include a…

By means of toric geometry we study hypersurfaces in weighted projective space of dimension four. In particular we compute for a given manifold its intrinsic topological coupling. We find that the result agrees with the calculation of the…

In the present paper we study subsolutions of the Dirac equation. The known examples of such subsolutions are the Weyl neutrino and the Majorana neutrino. It is shown that the Dirac equation for a massive non-interacting particle admits…

We characterize all projective K3 surfaces on which every integral pseudoeffective divisor admits an integral Zariski decomposition, using an explicit, terminating finite-step algorithm.

Conformally recurrent pseudo-Riemannian manifolds of dimension n>4 are investigated. The Weyl tensor is represented as a Kulkarni-Nomizu product. If the square of the Weyl tensor is nonzero, a covariantly constant symmetric tensor is…

In this paper we first note a result of birational automorphisms with bounded degree of projective varieties related with the Zariski dense orbit conjecture (ZDO) and the Zariski density of periodic points. Next, we give a reduced result of…

Magnetic and anomalous Hall conductivities induce anomalous transport features and novel optical phenomena in chiral systems. Here, we investigate reflection properties on the surface of a medium ruled by axion electrodynamics, which…

Considering bilayer systems as extensions of the planar ones by an internal space of two discrete points, we use the ideas of Noncommutative Geometry to construct the gauge theories for these systems. After integrating over the discrete…

We prove a discreteness result for the possible orders of harmonic maps from surfaces to Euclidean buildings; in particular for a building of type $W$ the order is of the form $\frac mk$ where $k$ divides $|W|$. This generalizes, in the…

Let A be a subspace arrangement and let chi(A,t) be the characteristic polynomial of its intersection lattice L(A). We show that if the subspaces in A are taken from L(B_n), where B_n is the type B Weyl arrangement, then chi(A,t) counts a…

The real cohomology of the space of imbeddings of S^1 into R^n, n>3, is studied by using configuration space integrals. Nontrivial classes are explicitly constructed. As a by-product, we prove the nontriviality of certain cycles of…

We examine maps between noncommutative projective spaces. A surjection of graded rings A-->A/J induces a closed immersion Proj(A/J)-->Proj(A). A homomorphism f:A-->B between graded rings induces an affine map U --> Proj(A) from a non-empty…

We study dimensions of the faces of the cone of nonnegative polynomials and the cone of sums of squares; we show that there are dimensional differences between corresponding faces of these cones. These dimensional gaps occur in all cases…

A smooth intersection $Y$ of two quadrics in $\mathbb{P}^{2g+1}$ has Hodge level 1. We show that such varieties $Y$ have a multiplicative Chow-K\"unneth decomposition, in the sense of Shen-Vial. As a consequence, a certain tautological…

In this article some noncommutative topological objects such as NC mapping cone and NC mapping cylinder are introduced. We will see that these objects are equipped with the NCCW complex structure of [PEDERSEN]. As a generalization we…

In this article, we discuss some recent developments of the Zariski Cancellation Problem in the setting of noncommutative algebras and Poisson algebras.

Based on a recent work by Thomas Bauer reproving the existence of Zariski decompositions for surfaces, we construct a b-divisorial analogue of Zariski decomposition in all dimensions.

Elements of noncommutative differential geometry of ${\mathbb Z}$-graded generalized Weyl algebras ${\mathcal A}(p;q)$ over the ring of polynomials in two variables and their zero-degree subalgebras ${\mathcal B}(p;q)$, which themselves are…

Conventional Weyl nodes are twofold band crossings that carry a unit monopole charge, which can exist in condensed matter systems with the protection of translation symmetry. Unconventional Weyl nodes are twofold/multifold band crossings…