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The Jacobian of a linear net of curves of order n is a curve of order 3(n-1). It passes through all points common to all curves of the net. It is the locus of points where ...

Given a set y=f(x) of n equations in n variables x_1, ..., x_n, written explicitly as y=[f_1(x); f_2(x); |; f_n(x)], (1) or more explicitly as {y_1=f_1(x_1,...,x_n); |; ...

The Jacobian group of a one-dimensional linear series is given by intersections of the base curve with the Jacobian curve of itself and two curves cutting the series.

The Jacobian conjecture in the plane, first stated by Keller (1939), states that given a ring map F of C[x,y] (the polynomial ring in two variables over the complex numbers ...

There are no fewer than three distinct notions of curve throughout mathematics. In topology, a curve is a one-dimensional continuum (Charatonik and Prajs 2001). In algebraic ...

The envelope of the lines connecting corresponding points on the Jacobian curve and Steinerian curve. The Cayleyian curve of a net of curves of order n has the same curve ...

The locus of points whose first polars with regard to the curves of a linear net have a common point. It is also the locus of points of concurrence of line polars of points ...

A quantity which transforms like a tensor except for a scalar factor of a Jacobian.

An algebraic curve over a field K is an equation f(X,Y)=0, where f(X,Y) is a polynomial in X and Y with coefficients in K. A nonsingular algebraic curve is an algebraic curve ...

A quintic curve is an algebraic curve of order five. Examples of quintic curves include the Burnside curve, butterfly catastrophe curve, and stirrup curve.