Ads
related to: singular points of a quadratic graph examples with steps and namesuslegalforms.com has been visited by 100K+ users in the past month
Search results
Results from the WOW.Com Content Network
Hence, it is technically more correct to discuss singular points of a smooth mapping here rather than a singular point of a curve. The above definitions can be extended to cover implicit curves which are defined as the zero set of a smooth function, and it is not necessary just to consider algebraic varieties. The definitions can be ...
Repeatedly blowing up the singular points of a curve will eventually resolve the singularities. The main task with this method is to find a way to measure the complexity of a singularity and to show that blowing up improves this measure. There are many ways to do this. For example, one can use the arithmetic genus of the curve.
The two families of lines on a smooth (split) quadric surface. In mathematics, a quadric or quadric hypersurface is the subspace of N-dimensional space defined by a polynomial equation of degree 2 over a field. Quadrics are fundamental examples in algebraic geometry. The theory is simplified by working in projective space rather than affine ...
In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas).It is a hypersurface (of dimension D) in a (D + 1)-dimensional space, and it is defined as the zero set of an irreducible polynomial of degree two in D + 1 variables; for example, D = 1 in the case of conic sections.
But it is important to note that a real variety may be a manifold and have singular points. For example the equation y 3 + 2x 2 y − x 4 = 0 defines a real analytic manifold but has a singular point at the origin. [2] This may be explained by saying that the curve has two complex conjugate branches that cut the real branch at the origin.
Consider a smooth real-valued function of two variables, say f (x, y) where x and y are real numbers.So f is a function from the plane to the line. The space of all such smooth functions is acted upon by the group of diffeomorphisms of the plane and the diffeomorphisms of the line, i.e. diffeomorphic changes of coordinate in both the source and the target.
The simplest example of singularities are curves that cross themselves. But there are other types of singularities, like cusps. For example, the equation y 2 − x 3 = 0 defines a curve that has a cusp at the origin x = y = 0. One could define the x-axis as a tangent at this point, but this definition can not be the same as the definition at ...
It was noticed in the formulation of Bézout's theorem that such singular points must be counted with multiplicity (2 for a double point, 3 for a cusp), in accounting for intersections of curves. It was then a short step to define the general notion of a singular point of an algebraic variety; that is, to allow higher dimensions.
Ads
related to: singular points of a quadratic graph examples with steps and namesuslegalforms.com has been visited by 100K+ users in the past month