Related papers: Weyl and Zariski chambers on projective surfaces

This is a survey on Zariski equisingularity. We recall its definition, main properties, and a variety of applications in Algebraic Geometry and Singularity Theory. In the first part of this survey, we consider Zariski equisingular families…

Let $X/K$ be a smooth projective variety defined over a number field, and let $f:X\to{X}$ be a morphism defined over $K$. We formulate a number of statements of varying strengths asserting, roughly, that if there is at least one point…

We discuss different generalizations of Zariski decomposition, relations between them and connections with finite generation of divisorial algebras.

In this paper, we continue the study of the relation between rational points of rational elliptic surfaces and plane curves. As an application, we give first examples of Zariski pairs of cubic-line arrangements that do not involve…

We define noncommutative minimal surfaces in the Weyl algebra, and give a method to construct them by generalizing the well-known Weierstrass-representation.

Given a root system, the Weyl chambers in the co-weight lattice give rise to a real toric variety, called the real toric variety associated to the Weyl chambers. We compute the integral cohomology groups of real toric varieties associated…

We state several questions, and prove some partial results, about the Chow ring $A^\ast(X)$ of complete intersections in projective space. For one thing, we prove that if $X$ is a general Calabi-Yau hypersurface, the intersection product…

Let V be a normal affine surface which admits a C*- and a C+-action. In this note we show that in many cases V can be embedded as a principal Zariski open subset into a hypersurface of a weighted projective space. In particular, we recover…

We characterize the integral Zariski decomposition of a smooth projective surface with Picard number 2 to partially solve a problem of B. Harbourne, P. Pokora, and H. Tutaj-Gasinska [Electron. Res. Announc. Math. Sci. 22 (2015), 103--108].

In this paper, we study the geometry of two-torsion points of elliptic curves in order to distinguish the embedded topology of reducible plane curves consisting of a smooth cubic and its tangent lines. As a result, we obtain a new family of…

Consider a finite collection of affine hyperplanes in $\mathbb R^d$. The hyperplanes dissect $\mathbb R^d$ into finitely many polyhedral chambers. For a point $x\in \mathbb R^d$ and a chamber $P$ the metric projection of $x$ onto $P$ is the…

This is the first part of our work on Zariski decomposition structures, where we study Zariski decompositions using Legendre-Fenchel type transforms. In this way we define a Zariski decomposition for curve classes. This decomposition…

In this paper, we want to discuss the topology of the non-singular hypersurface $Y^{n}$ with complex dimension $n$ in a projective toric manifold $X^{n+1}$. When $n$ is odd, our main results are a decomposition of $Y^{n}\cong Y'\sharp \…

A Klein surface is a surface with a dianalytic structure. A double of a Klein surface $X$ is a Klein surface $Y$ such that there is a degree two morphism (of Klein surfaces) $Y\rightarrow X$. There are many doubles of a given Klein surface…

We study the polyhedral geometry of the hyperplanes orthogonal to the weights of the first and the second fundamental representations of $sl_n$ inside the dual fundamental Weyl chamber. We obtain generating functions that enumerate the…

Given a rational elliptic surface X over an algebraically closed field, we investigate whether a given natural number k can be the intersection number of two sections of X. If not, we say that k a gap number. We try to answer when gap…

The Weyl-Wigner correspondence prescription, which makes large use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for noncommutative Fourier analysis allowing for that property. It is…

Given a projective hyper-K\"ahler manifold $X$, we study the asymptotic base loci of big divisors on $X$. We provide a numerical characterization of these loci and study how they vary while moving a big divisor class in the big cone, using…

We enumerate, via floor diagrams, complex and real curves in the projective plane blown up in $n$ points on a conic. As an application, we deduce Gromov-Witten and Welschinger invariants of Del Pezzo surfaces. These results are mainly…

The purpose of this paper is to study the reflections of a convex body. In particular, we are interested in orthogonal reflections of its sections that can be extended to reflections of the whole body. For this reason, we need to study the…