Related papers: Cylinders in rational surfaces
We obtain an explicit formula for the number of rational cuspidal curves of a given degree on a del-Pezzo surface that pass through an appropriate number of generic points of the surface. This enumerative problem is expressed as an Euler…
We study the structure of complex points on real surfaces, embedded into complex Elliptic surfaces. We show, for example, that any compact surface has a totally real embedding into a blow-up of a K3 surface. We also exhibit smooth disc…
We investigate CMC-surfaces with periodic metric in a dressing orbit of the cylinder. It is shown, that such surfaces are always of finite type. Using the periodicity conditions for the extended frame of a CMC-surface, we develop an…
We produce several algebraic curves, some well--known, some new, out of circles, by means of two classical (mutually reciprocal) algebraic methods: blow--down and blow--up.
In this paper, we study dilation of cyclic polytopes with the vertices defined by a generator of the simplest cubic fields. In particular, for a specific range of values, we give a precise number of the contained lattice points.
We study the problem of resolving singularities via the blow-up of the module of derivations. Our main results are a positive answer for the case of curves and log-canonical surface singularities, i.e., a finite sequence of blow-ups along…
This paper proposes a simple technique of curve and surface construction with B-splines. Given a control polygon or a control mesh together with node ordinates corresponding to all control points, a rational curve or surface is obtained by…
A formula for the radii and positions of four circles in the plane for an arbitrary linearly independent circle configuration is found. Among special cases is the recent extended Descartes Theorem on the Descartes configuration and an…
Utilizing a splitting of geometric flows on surfaces introduced by Buzano and Rupflin, we present a general scheme to prove blow up criteria for such geometric flows. A vital ingredient is a new compactness theorem for families of metrics…
We utilise the two principles of decoupling introduced in [arXiv:2407.16108] to prove decoupling for two types of surfaces exhibiting radial symmetry. The first type are surfaces of revolution in $\mathbb R^n$ generated by smooth surfaces…
Cylinders in projective varieties play an important role in connection with unipotent group actions on certain affine algebraic varieties. The previous work due to Dubouloz and Kishimoto deals with the condition for a del Pezzo fibration to…
A soft, thin, elastomeric micro-cylinder is induced to roll on a solid substrate by releasing small quantity of a solvent. The solvent swells the cylinder asymmetrically at one side and evaporates out of it from where it is exposed to…
Our main goal is to give a sense of recent developments in the (stable) rationality problem from the point of view of unramified cohomology and 0-cycles as well as derived categories and semiorthogonal decompositions, and how these…
We prove that the Euler-Chow series for ruled surfaces and scrolls is rational by means of an explicit computation.
A cyclic random motion at finite velocity with orthogonal directions is considered in the plane and in $\mathbb{R}^3$. We obtain in both cases the explicit conditional distributions of the position of the moving particle when the number of…
We study the geometry of spaces of planes on smooth complete intersections of three quadrics, with a view toward rationality questions.
We compute small rational models for configuration spaces of points on oriented surfaces, as right modules over the framed little disks operad. We do this by splitting these surfaces in unions of several handles. We first describe rational…
The paper is concerned with the problem on rolling of a homogeneous ball on an arbitrary surface. New cases when the problem is solved by quadratures are presented. The paper also indicates a special case when an additional integral and…
Let X be a smooth irreducible projective surface. The aim of this paper is to establish a version of Clifford's theorem for coherent systems on X.
By the famous ADE classification rational double points are simple. Rational triple points are also simple. We conjecture that the simple normal surface singularities are exactly those rational singularities, whose resolution graph can be…