Search Results for ""

The dimension of a special series can never exceed half its order.

A crunode, also known as an ordinary double point, of a plane curve is point where a curve intersects itself so that two branches of the curve have distinct tangent lines. ...

One of the Plücker characteristics, defined by p=1/2(n-1)(n-2)-(delta+kappa)=1/2(m-1)(m-2)-(tau+iota), where m is the class, n the order, delta the number of nodes, kappa the ...

A closed embedded smooth plane curve has at least four vertices, where a vertex is defined as an extremum of curvature.

If a sequence of double points is passed as a closed curve is traversed, each double point appears once in an even place and once in an odd place.

H=|aa^'a^('')|a_(x^(n-2))a_(x^(n-2))^'a_(x^(n-2))^('')=0. The nonsingular inflections of a curve are its nonsingular intersections with the Hessian.

Every modular system has a modular system basis consisting of a finite number of polynomials. Stated another way, for every order n there exists a nonsingular curve with the ...

The necessary and sufficient condition that an algebraic curve has an algebraic involute is that the arc length is a two-valued algebraic function of the coordinates of the ...

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 ...

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.