Rational curves with cusps

Geometric Discriminate Methods of a Class of Quartic Offset-rational Curves

Journal of Computer-Aided Design & Computer Graphics ◽

10.3724/sp.j.1089.2018.16368 ◽

2018 ◽

Vol 30 (3) ◽

pp. 499

Author(s):

Xiaojuan Duan ◽

Guozhao Wang

Keyword(s):

Rational Curves

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Non Kählerian surfaces with a cycle of rational curves

Complex Manifolds ◽

10.1515/coma-2020-0114 ◽

2021 ◽

Vol 8 (1) ◽

pp. 208-222

Author(s):

Georges Dloussky

Keyword(s):

Deformation Theory ◽

Complex Surface ◽

Rational Curves ◽

Intersection Form ◽

Connected Component ◽

Hirzebruch Surface ◽

Compact Complex Surface ◽

A Chain

Abstract Let S be a compact complex surface in class VII0 + containing a cycle of rational curves C = ∑Dj . Let D = C + A be the maximal connected divisor containing C. If there is another connected component of curves C ′ then C ′ is a cycle of rational curves, A = 0 and S is a Inoue-Hirzebruch surface. If there is only one connected component D then each connected component Ai of A is a chain of rational curves which intersects a curve Dj of the cycle and for each curve Dj of the cycle there at most one chain which meets Dj . In other words, we do not prove the existence of curves other those of the cycle C, but if some other curves exist the maximal divisor looks like the maximal divisor of a Kato surface with perhaps missing curves. The proof of this topological result is an application of Donaldson theorem on trivialization of the intersection form and of deformation theory. We apply this result to show that a twisted logarithmic 1-form has a trivial vanishing divisor.

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Two algebraic deformations of a K3 surface

Nagoya Mathematical Journal ◽

10.1017/s0027763000019267 ◽

1981 ◽

Vol 82 ◽

pp. 1-26

Author(s):

Daniel Comenetz

Keyword(s):

Hyperelliptic Curve ◽

Double Cover ◽

Rational Curves ◽

K3 Surface ◽

Quartic Surface ◽

Quadric Cone ◽

Birational Model ◽

Affine Line ◽

Characteristic 2 ◽

General Member

Let X be a nonsingular algebraic K3 surface carrying a nonsingular hyperelliptic curve of genus 3 and no rational curves. Our purpose is to study two algebraic deformations of X, viz. one specialization and one generalization. We assume the characteristic ≠ 2. The generalization of X is a nonsingular quartic surface Q in P3 : we wish to show in § 1 that there is an irreducible algebraic family of surfaces over the affine line, in which X is a member and in which Q is a general member. The specialization of X is a surface Y having a birational model which is a ramified double cover of a quadric cone in P3.

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A POSITIVITY PROPERTY FOR FOLIATIONS ON COMPACT KÄHLER MANIFOLDS

International Journal of Mathematics ◽

10.1142/s0129167x06003333 ◽

2006 ◽

Vol 17 (01) ◽

pp. 35-43 ◽

Cited By ~ 16

Author(s):

MARCO BRUNELLA

Keyword(s):

Kähler Manifold ◽

Rational Curves ◽

Kähler Manifolds ◽

Kahler Manifolds ◽

Canonical Bundle ◽

Positivity Property ◽

Kahler Manifold ◽

Compact Kähler Manifold

We prove that the canonical bundle of a foliation by curves on a compact Kähler manifold is pseudoeffective, unless the foliation is a (special) foliation by rational curves.

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Robot Trajectory Planning Using Rational Frenet-Serret Curves

Volume 2 ◽

10.1115/esda2004-58410 ◽

2004 ◽

Author(s):

Reza Ravani ◽

Ali Meghdari

Keyword(s):

Trajectory Planning ◽

Computer Animation ◽

Rational Curves ◽

Robot Arm ◽

Robot Trajectory ◽

Arm Motion ◽

Sweep Surface ◽

And Robotics ◽

Rotation Minimizing Frame ◽

Robot Trajectory Planning

The aim of this paper is to demonstrate that the techniques of Computer Aided Geometric Design such as spatial rational curves and surfaces could be applied to Kinematics, Computer Animation and Robotics. For this purpose we represent a method which utilizes a special class of rational curves called Rational Frenet-Serret (RF) [8] curves for robot trajectory planning. RF curves distinguished by the property that the motion of their Frenet-Serret frame is rational. We describe an algorithm for interpolation of positions by a rational Frenet-Serret motion. Further more we provide an analysis on spatial frames (Frenet-Serret frame and Rotation Minimizing frame) for smooth robot arm motion and investigate their applications in sweep surface modeling.

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