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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 ...

Given two univariate polynomials of the same order whose first p coefficients (but not the first p-1) are 0 where the coefficients of the second approach the corresponding ...

A product of a reflection in a line and translation along the same line.

If two groups are residual to a third, every group residual to one is residual to the other. The Gambier extension of this theorem states that if two groups are ...

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 ...

A line making equal angles with the edges of a trihedron is called an isoclinal line of the trihedron.

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.

Using Clebsch-Aronhold notation, an algebraic curve satisfies xi_1^na_y^n+xi_1^(n-1)xi_2a_y^(n-1)a_x+1/2n(n-1)xi_1^(n-2)xi_2^2a_y^(n-2)a_x^2+... ...