Singular points of transformations and two-parameter families of curves

Singular Points of Plane Curves

ly isomorphic to (C×)r−1 × (C), and hence also to (S1)r−1 × (R), where r = |J | is the number of branches and k = δ(C)− r+1 = 1 2 (μ(C) + 1 − r). The construction of the Jacobian variety J(C̃) of the non-singular curve C̃ in the large is standard in algebraic geometry. There is also a notion of Jacobian of a singular curve C , defined e.g. in [85], which, like the other, is an abelian group. Ther...

Integer points on two families of elliptic curves

In this paper we find all the integer points on elliptic curves induced by the Diophantine triples {k − 1, k + 1, 16k − 4k} and {k − 1, k + 1, 64k− 48k + 8k} that have either rank two or 2 ≤ k ≤ 10000 (with one possible exception).

The Geometry of Families of Singular Curves

a comparative analysis of the marginal microleakages of two pit and fissure sealans, conseal-f and conseal clear

چکیده ندارد.

Computing singular points of plane rational curves

We compute the singular points of a plane rational curve, parametrically given, using the implicitization matrix derived from the μ-basis of the curve. It is shown that singularity factors, which are defined and uniquely determined by the elementary divisors of the implicitization matrix, contain all the information about the singular points, such as the parameter values of the singular points ...