Related papers: A remark on hyperplane sections of rational normal…
In this article we prove in the main theorem that, there is a bijection between the isomorphism classes of a certain type of real hyperplane arrangements on the one hand, and the antipodal pairs of convex cones of an associated…
Symplectic and complex toric quasifolds are a generalization of toric manifolds and orbifolds to the nonrational case. In this paper, we reframe these notions from the viewpoint of algebraic geometry.
By changing to an orthogonal basis, we give a short proof that the subfactor of the graded algebra of a planar algebra reproduces the planar algebra.
This is a survey on the Fano schemes of linear spaces, conics, rational curves, and curves of higher genera in smooth projective hypersurfaces, complete intersections, Fano threefolds, etc.
We present a theory that produces several examples where the homotopy Lie algebra of a complex hyperplane arrangement is not finitely presented. We also present examples of hyperplane arrangements where the enveloping algebra of this Lie…
Rational homology ellipsoids are certain Liouville domains diffeomorphic to rational homology balls and having Lagrangian pin-wheels as their skeleta. From the point of view of almost toric fibrations, they are a natural generalisation of…
This note is a survey on the topology of hyperplane arrangements. We mainly focus on the relationship between topology and the real structure, such as adjacent relations of chambers and stratifications related to real structures.
We study cubic rational maps that take lines to plane curves. A complete description of such cubic rational maps concludes the classification of all planarizations, i.e., maps taking lines to plane curves.
We give a geometrical characterization of the ideal of quadrics containing a canonical curve with an involution. This implies to study involutions of rational normal scrolls and Veronese surfaces.
We completely classify all plane curves of degree at most 30 with a unique cuspidal (locally unibranch) singular point and rational normalization in terms of the Newton pairs parameterizing the cusp. We distinguish between prime and…
We complete the classification of hyperelliptic threefolds, describing in an elementary way the hyperelliptic threefolds with group $D_4$. These are algebraic and form an irreducible 2-dimensional family. Our paper is fully self-contained.
We classify $G$-solid rational surfaces over the field of complex numbers.
In this work we compute the Stokes matrices of the ordinary differential equation satisfied by the hypergeometric integrals associated to an arrangement of hyperplanes in generic position. This generalizes the computation done by Ramis and…
We introduce normal cores, as well as the more general action cores, in the context of a semi-abelian category, and further generalise those to split extension cores in the context of a homological category. We prove that, if the category…
We study the hyperplane arrangements associated, via the minimal model programme, to symplectic quotient singularities. We show that this hyperplane arrangement equals the arrangement of CM-hyperplanes coming from the representation theory…
Ballico proved that a smooth projective variety $X$ of degree $d$ over a finite field of $q$ elements admits a smooth hyperplane section if $q\geq d(d-1)^{\dim X}$. In this paper, we refine this criterion for higher codimensional linear…
The paper gives some criteria for partial sums of rational number sequences to be not rational functions and to be not algebraic functions. As an application, we study partial sums of some famous rational number sequences in mathematical…
For every $d\geq 2$, we construct a subset $D\subseteq \{1,2,\dots,n\}^d$ of size $n-o(n)$ such that every affine hyperplane of $\mathbb{R}^d$ intersects $D$ in at most $d$ points, and every hypersphere of $\mathbb{R}^n$ intersects $D$ in…
We establish some upper and lower bounds of the rational topological complexity for certain classes of elliptic spaces. Our techniques permit us in particular to show that the rational topological complexity coincides with the dimension of…
In this exposition, we get examples of what is called a "linear hyperdoctrine", based on categories of comodules indexed by coalgebras. This structures can model first order linear logic.