Cusp (singularity) - Wikipedia
In mathematics, a cusp, sometimes called spinode in old texts, is a point on a curve where a moving point must reverse direction. A typical example is given in the figure. A cusp is thus a type of singular point of a curve. For a plane curve defined by an analytic, parametric equation.
Nodal and cuspidal curves - Purdue University
To get a better feeling for what this ought to look like, form the intersection of our cusp with a small sphere ∣x∣2 + ∣y∣2 = ε 2. This is called the link of the singularity. The sphere can be identified with R3 plus a point at infinity, and the link is a knot in this space.
Hyperelliptic Curves and Cusps - Purdue University
To get a better feeling for what this ought to look like, form the intersection of our cusp with a small sphere ∣x∣2 + ∣y∣2 = ε 2. This is called the link of the singularity. The sphere can be identified with R3 plus a point at infinity, and the link is a knot in this space.
11.2.2 Classification of singularities - Massachusetts Institute of ...
There are two types of singularities on the offset curves of a regular progenitor curve, irregular points and self-intersections. Irregular points include isolated points and cusps. A point on a curve is called an isolated point of if there is no other point of in some neighborhood of .
Cusp (singularity) - CSDN博客
2022年12月10日 · An ordinary cusp is given by {\displaystyle x {2}-y {3}=0,}{\displaystyle x {2}-y {3}=0,} i.e. the zero-level-set of a type A2-singularity. Let f (x, y) be a smooth function of x and y and assume, for simplicity, that f (0, 0) = 0. Then a type A2-singularity of f at (0, 0) can be characterised by:
In this paper I answer a question asked by Neumann and Wahl about coverings of cusp singularities. In Proposition 4.1 of [5], they prove that there exist cusps with no abelian cover by a complete intersection, and go on to conjecture that some cusps have no Galois cover by a complete intersection.
singularity. The embedding dimension is equal to the smallest dimension of any smooth germ (M; q) such that . embed. M is smooth. As TpX TpM, and the dimension of M is equal to the dimension of TpM, it is clear that the dimension of M .
Cusp (singularity) - Wikiwand
In mathematics, a cusp, sometimes called spinode in old texts, is a point on a curve where a moving point must reverse direction. A typical example is given in the figure. A cusp is thus a type of singular point of a curve.
On the Frobenius manifolds for cusp singularities - ScienceDirect
2015年3月19日 · We show that the Frobenius manifold associated to the pair of a cusp singularity and its canonical primitive form is isomorphic to the one constructed from the Gromov–Witten theory for an orbifold projective line with at most three orbifold points. We also calculate the intersection form of the Frobenius manifold.
existence of a smoothing of a cusp singularity. In the notation of Sect. 1, let V be the singular Inoue-Hirzebruch surface with two dual cusps D and D'; let the corresponding singular points of ~ be p and p'.
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