Elements of the Theory of Algebraic Curves

a₁ algebraic curves arbitrary assume Bezout's Theorem birational branches centered C₁ c₁X C₂ called Chapter coefficients common conic containing coordinate system Corollary cross-ratio cycle defined definition degree distinct double point E₁ E₂ effective divisors equation F(Xo F₁ field finite distance finite number g₁ genus given H₁ Hence hyperplane induction infinitely infinitely near point intersection multiplicity irreducible curve Lemma Let F line at infinity linear series linearly independent locally quadratic transformation m₁X monic Moreover morphism nonsingular cubic nonunit number of points one-to-one correspondence ordinary singularities P₁ P₂ pass point of inflection power series primitive branch representation projective plane prove quadratic transformation r-fold point r₁ rational function ring similarly simple point suppose t₁ tangent Theorem unique factorization domain valuation vanishes whence write X₁ y₁