Plane Algebraic Curves

abelian affine algebraic curves analytic set analytic set germ Bézout's theorem braid branches choose circle coefficients compute consider construction corresponding cubic curve germs cycles decomposition defined definition described differential forms dimension divisor double point dual equivalent example exceptional curve fibration fibre finitely follows genus geometry hence holomorphic functions homeomorphic homogeneous coordinates homogeneous polynomials homology class infinitely near points inflection points intersection multiplicity intersection numbers intersection points investigation irreducible components irreducible curve isomorphism l-dimensional Lemma linear system manifold mapping Milnor multiplicity sequences neighbourhood Newton polygon nonsingular normal form o-processes obtain parabola plane curve polydisc preimage projective plane Proof Proposition prove Puiseux expansion Puiseux pairs quadratic transformation quadric resolution graph resolution of singularities resp Riemann singular points solution surface tangent tion topological torus knot triangle TURK's-HEAD vanish Weierstrass zero set