相关论文: Equations of Parametric Surfaces via Syzygies

It is shown that the question raised in Section 5.7 of [1] has an affirmative answer.

In a previous work of the authors, a result to algorithmically compute the topology types of the level curves of an algebraic surface, is given. From this result, here we derive applications based on level curves to determine some…

The translation is not verbatim, many parts have been abbreviated and in some case alternative proofs were devised emphasizing intuition.

This work consists of two parts. In the first part we develop new techniques to compute Koszul cohomology groups for several classes of varieties. As applications we prove results on projective normality and syzygies for algebraic surfaces.…

This paper presents new examples of projective surfaces of general type over $\mathbb{C}$ with canonical map of degree $ 3 $ onto a surface of general type. Very few examples are known of such surfaces and some of the examples in this paper…

Many algorithms for surface registration risk producing significant errors if surfaces are significantly nonisometric. Manifold learning has been shown to be effective at improving registration quality, using information from an entire…

We report about significant enhancements of the complex algebraic geometry theorem proving subsystem in GeoGebra for automated proofs in Euclidean geometry, concerning the extension of numerous GeoGebra tools with proof capabilities. As a…

In this paper we define and construct a new class of algebraic surfaces in three-dimensional Euclidean space generated by a curve and a congruence of circles. We study their properties and visualize them with the program Mathematica.

We formulate several conjectures which shed light on the structure of Veronese syzygies of projective spaces. Our conjectures are based on experimental data that we derived by developing a numerical linear algebra and distributed…

This article derives closed-form parametric formulas for the Minkowski sums of convex bodies in d-dimensional Euclidean space with boundaries that are smooth and have all positive sectional curvatures at every point. Under these conditions,…

In many applications free surface flow through rigid porous media has to be modeled. Examples refer to coastal engineering applications as well as geotechnical or biomedical applications. Albeit the frequent applications, slight…

This paper aims to develop the mathematical representation of a surface generated by elliptical arcs joining the sides of a regular polygon to a point lying vertically upward on the central axis of the polygon. The volume of the…

We construct flat metrics in a given conformal class with prescribed singularities of real orders at marked points of a closed real surface. The singularities can be small conical, cylindrical, and large conical with possible translation…

Surfaces of revolution in three-dimensional Euclidean space are considered. Several new examples of surfaces of revolution associated with well-known solvable cases of the Schoedinger equation (infinite well, harmonic oscillator, Coulomb…

Cayley's (ruled cubic) surface carries a three-parameter family of twisted cubics. We describe the contact of higher order and the dual contact of higher order for these curves and show that there are three exceptional cases.

We derive level set version of partial uniform ellipticity for symmetric concave functions. This suggests an effective approach to investigate second order fully nonlinear equations of elliptic and parabolic type.

Subdivision surfaces are proven to be a powerful tool in geometric modeling and computer graphics, due to the great flexibility they offer in capturing irregular topologies. This paper discusses the robust and efficient implementation of an…

This proves Kontsevich's mirror conjecture for (on the symplectic side) a quartic surface in P^3.

We establish a family of parametric isoperimetric-type inequalities with multiple geometric quantities for closed convex curves. These inequalities hold under certain parameter conditions. We also prove the equality conditions. Some new…

This paper constructs a Riemann surface associated to the icosahedron and discusses the geodesics associated to a flat metric on this surface. Because of the icosahedral symmetry, this is a distinguished special case of the example treated…