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The branch of algebraic topology which deals with homotopy groups. Homotopy methods can be used to solve systems of polynomials by embedding the polynomials in a family of ...

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.

Any linear system of point-groups on a curve with only ordinary singularities may be cut by adjoint curves.

If two curves phi and psi of multiplicities r_i!=0 and s_i!=0 have only ordinary points or ordinary singular points and cusps in common, then every curve which has at least ...

Any irreducible curve may be carried by a factorable Cremona transformation into one with none but ordinary singular points.

An adjoint curve which bears a special relation to the base curve.

A subvariety of an algebraic variety that is not the entire variety. The proper subvarieties of a line are its nonempty finite subsets, the proper subvarieties of a plane are ...

If a fixed point is added to each group of a special complete series, then the resulting series is complete.

Associated with an irreducible curve of curve genus p, there are p linearly independent integrals of the first sort. The roots of the integrands are groups of the canonical ...

If the difference between the order and the dimension of a series is less than the curve genus, then the series is special.