Related papers: Conic and Quadric surfaces
In this paper we consider plane quartics with to involutions. We compute the Dixmier invariants, the bitangents and the Matrix representation problem of these curves, showing that they have symbolic solutions for the last two questions.
In this paper we present algorithms for computing the topology of planar and space rational curves defined by a parametrization. The algorithms given here work directly with the parametrization of the curve, and do not require to compute or…
The two-dimensional Dirac equation has been widely used in graphene physics, the surface of topological insulators, and especially quantum scarring. Although a numerical approach to tackling an arbitrary confining problem was proposed…
We study and classify linearly normal surfaces in $\mathbf{P}^n$, of degree $d$ and sectional genus $g$, such that $d\geq 2g-1$.
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
We make a systematic study of the focal surface of a congruence of lines in the projective space. Using differential techniques together with techniques from intersection theory, we reobtain in particular all the invariants of the focal…
We study the shape of inflated surfaces introduced in \cite{B1} and \cite{P1}. More precisely, we analyze profiles of surfaces obtained by inflating a convex polyhedron, or more generally an almost everywhere flat surface, with a symmetry…
Coarse geometry, the branch of topology that studies the global properties of spaces, was originally developed for metric spaces and then Roe introduced coarse structures as a large-scale counterpart of uniformities. In the literature,…
We construct a polynomial planar vector field of degree two with one invariant algebraic curves of large degree. We exhibit an explicit quadratic vector fields which invariant curves of degree nine, twelve, fifteen and eighteen degree.
Here one will find a rigorous treatment of the simplest situation in Surface Area Theory, viz. the nonparametric case with domain the unit square in the plane. This is installment IV of a four part discussion of certain aspects of Real…
We study geodesics on the parameter manifold, for systems exhibiting second order classical and quantum phase transitions. The coupled non-linear geodesic equations are solved numerically for a variety of models which show such phase…
Given a minimal surface equipped with a generically finite map to an Abelian variety, we give an optimal bound on the canonical degree of a rational or an elliptic curve. As a corollary, we obtain the finiteness of rational and elliptic…
It is still a challenging task of today to recognize the type of a given algebraic surface which is described only by its implicit representation. In~this paper we will investigate in more detail the case of canal surfaces that are often…
This is a first graduate course in algebraic geometry. It aims to give the student a lift up into the subject at the research level, with lots of interesting topics taken from the classification of surfaces, and a human-oriented discussion…
We present a complete classification of complex plane algebraic curves, equipped with the induced Euclidean, up to global bilipschitz homeomorphism.
Surfaces with concentric $K$-contours and parallel $K$-contours in Euclidean $3$-space are defined. Crucial examples are presented and characterization of them are given.
We study a class of complex polynomial equations on a finite graph with a view to understanding how holistic phenomena emerge from combinatorial structure. Particular solutions arise from orthogonal projections of regular polytopes,…
Surfaces and curves play an important role in geometric design. In recent years, problem of finding a surface passing through a given curve have attracted much interest. In the present paper, we propose a new method to construct a surface…
In this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups. We give applications to the classification of real…
For spacelike stationary (i.e. zero mean curvature) surfaces in 4-dimensional Lorentz space one can naturally introduce two Gauss maps and Weierstrass representation. In this paper we investigate their global geometry systematically. The…