Related papers: Quartic unexpected curves and surfaces

We report on recent results concerning the construction of curves on K3 surfaces: the proof of the Tate conjecture for K3 surfaces in odd characteristic (after Maulik, Charles and Madapusi Pera), and the construction of infinitely many…

In [15] Labourie develops a theory of immersed surfaces of prescribed extrinsic curvature which has since found widespread applications in hyperbolic geometry, general relativity, Teichm\"uller theory, and so on. In this chapter, we present…

In this paper we describe projective curves and surfaces such that almost all their hyperplane sections are projectively equivalent. Our description is complete for curves and close to being complete for smooth surfaces. In the appendix we…

We study an isomorphism between the group of rigid body displacements and the group of dual quaternions modulo the dual number multiplicative group from the viewpoint of differential geometry in a projective space over the dual numbers.…

In this paper, we classify the configurations of the singular points which appear on the quotients of the projective plane by the $1$-foliations of degree $-1$ in characteristic $2$.

Since the end of the 19th century, and after the works of F. Klein and H. Poincar\'e, it is well known that models of elliptic geometry and hyperbolic geometry can be given using projective geometry, and that Euclidean geometry can be seen…

We study quartic surfaces that admit a group of projective automorphisms isomorphic to icosahedron group.

In this survey article we give a brief account of constructions and results concerning the quivers with potentials associated to triangulations of surfaces with marked points. Besides the fact that the mutations of these quivers with…

This note being devoted to some aspects of the inverse problem of representation theory contains a new insight into it illustrated by two topics. The attention is concentrated on the manner of representation of abstract objects by the…

The quantum deformation $CP_q(N)$ of complex projective space is discussed. Many of the features present in the case of the quantum sphere can be extended. The differential and integral calculus is studied and $CP_q(N)$ appears as a quantum…

We construct new examples of singular projective plane curves whose complements have finite and non-abelian fundamental groups, by generalizing the classical three cuspidal quartic curve discovered by Zariski.

In this work, we present an adaptation of the classical stereographic projection, originally formulated for the sphere, now considering the context of the ellipsoid and the elliptic paraboloid. We begin by constructing the stereographic…

Quadratic residue patterns modulo a prime are studied since 19th century. In the first part we extend existing results on the number of consecutive $\ell$-tuples of quadratic residues, studying corresponding algebraic curves and their…

The aim of this paper is to give some characterizations for N-Legendre and N-slant curves in the unit tangent bundles of surfaces endowed with natural diagonal lifted structures.

We classify singular Enriques surfaces in characteristic two supporting a rank nine configuration of smooth rational curves. They come in one-dimensional families defined over the prime field, paralleling the situation in other…

We study twists of the Burkhardt quartic threefold over non-algebraically closed base fields of characteristic different from 2,3,5. We show they all admit quartic models in projective four-space. We identify a Galois-cohomological…

We give a complete classification of Q_l-cohomology projective planes with isolated ADE-singularities and numerically trivial canonical bundle in odd characteristic. This leads to a beautiful relation with certain Enriques surfaces which…

This paper provides an overview of selected results and open problems in the theory of hyperplane arrangements, with an emphasis on computations and examples. We give an introduction to many of the essential tools used in the area, such as…

The purpose of the present note is to provide a new proof ot the well-known result due to Hartshorne and Hirschowitz to the effect that general lines in projective spaces have good postulation. Our approach uses specialization to a…

We construct special conics configurations from some points configurations which are the singularities of the dual of a quartic curve.