Related papers: Topology of plane algebraic curves: the algebraic …
In this article we give an implementation of the standard algorithm to segment a real algebraic plane curve defined implicitly. Our implementation is efficient and simpler than previous. We use global information to count the number of…
In this article we look at a scroll of $PG(6,q)$ that uses a projectivity to rule a conic and a twisted cubic. We show this scroll is a ruled quintic surface $\mathcal V^5_2$, and study its geometric properties. The motivation in studying…
Free actions of finite groups on spheres give rise to topological spherical space forms. The existence and classification problems for space forms have a long history in the geometry and topology of manifolds. In this article, we present a…
This is a survey paper on Alegbraic Geometry over Lie Algebras
We show how the computer algebra system OSCAR can be used to obtain topologically correct or visually pleasing drawings of real plane algebraic curves.
We give a combinatorial description of closed curves on oriented surfaces in terms of certain permutations, called charts. We describe automorphisms of curves in terms of charts and compute the total number of curves counted with…
The action of ring automorphisms of the polynomial ring in two variables over the real numbers on real plane curves is considered. The orbits containing degree-three polynomials are computed, with one representative per orbit being…
We present a variety of geometrical and combinatorial tools that are used in the study of geometric structures on surfaces: volume, contact, symplectic, complex and almost complex structures. We start with a series of local rigidity results…
We classify endomorphisms of the plane that preserve a pencil of curves.
We consider two algebras of curves associated to an oriented surface of finite type - the cluster algebra from combinatorial algebra, and the skein algebra from quantum topology. We focus on generalizations of cluster algebras and…
We study the plane automorphisms given by polynomials with certain degree decompositions.
The paper gives topological as well as rigid isotopy classification of smooth irreducible algebraic curves in the real projective 3-space for the case when the degree of the curve is at most six and its genus is at most one.
For affine algebraic plane curves we reduce a calculation of its invariants to calculation of the intersection of kernels of some derivations.
We take a categorical approach to describe ternary derivations and ternary automorphisms of triangular algebras. New classes of automorphisms and derivations of triangular algebras are also introduced and studied.
Surfaces and curves play an important role in geometric design. In recent years, problem of finding a surface passing through a given curve has attracted much interest. In the present paper, we propose a new method to construct a surface…
We define a topological invariant of complex projective plane curves. As an application, we present new examples of arithmetic Zariski pairs.
This survey paper describes the role of splines in geometry and topology, emphasizing both similarities and differences from the classical treatment of splines. The exposition is non-technical and contains many examples, with references to…
In this pages I give an overview of the relationship between Model Theory, Arithmetic and Algebraic Geometry. The topics will be the basic ones in the area, so this is just an invitation, in the presentation of topics I mainly follow the…
A criterion for the existence of a birational embedding of an algebraic curve into a projective plane with two Galois points is presented. Several novel examples of plane curves with two inner Galois points as an application are described.
We discuss solutions of several questions concerning the geometry of conformal planes.