| C. G. Gibson is Senior Fellow in Mathematical Sciences, University of Liverpool... .. << 查看详细 |
| list of illustrations . list of tables preface 1 real algebraic curves 1.1 parametrized and implicit curves 1.2 introductory examples 1.3 curves in planar kinematics 2 general ground fields 2.1 two motivating examples 2.2 groups, rings and fields 2.3 general affine planes and curves 2.4 zero sets of algebraic curves 3 polynomial algebra 3.1 factorization in domains 3.2 polynomials in one variable 3.3 polynomials in several variables 3.4 homogeneous polynomials 3.5 formal differentiation 4 afiine equivalence 4.1 affine maps .4.2 affine equivalent curves 4.3 degree as an affine invariant 4.4 centres as affine invariants 5 affine conics 5.1 affine classification 5.2 the delta invariants 5.3 uniqueness of equations 6 singularities of affine curves 6.1 intersection numbers 6.2 multiplicity of a point on a curve 6.3 singular points 7 tangents to affine curves 7.1 generalities about tangents 7.2 tangents at simple points 7.3 tangents at double points 7.4 tangents at points of higher multiplicity 8 rational affine curves 8.1 rational curves 8.2 diophantine equations 8.3 conics and integrals 9 projective algebraic curves 9.1 the projective plane 9.2 projective lines 9.3 affine planes in the projective plane 9.4 projective curves 9.5 affine views of projective curves 10 singularities of projective curves 10.1 intersection numbers 10.2 multiplicity of a point on a curve .. 10.3 singular points 10.4 delta invariants viewed projectively 11 projective equivalence 11.1 projective maps 11.2 projective equivalence 11.3 projective conics 11.4 affine and projective equivalence 12 projective tangents 12.1 tangents to projective curves 12.2 tangents at simple points 12.3 centres viewed projectively 12.4 foci viewed projectively 12.5 tangents at singular points 12.6 asymptotes 13 flexes 13.1 hessian curves 13.2 configurations of flexes 14 intersections of projective curves 14.1 the geometric idea 14.2 resultants in one variable 14.3 resultants in several variables 14.4 bezout's theorem 14.5 the multiplicity inequality 14.6 invariance of the intersection number 15 projective cubics 15.1 geometric types of cubics 15.2 cubics of general type 15.3 singular irreducible cubics 15.4 reducible cubics 16 linear systems 16.1 projective spaces of curves 16.2 pencils of curves 16.3 solving quartic equations 16.4 subspaces of projective spaces 16.5 linear systems of curves 16.6 dual curves 17 the group structure on a cubic 17.1 the nine associated points 17.2 the star operation 17.3 cubics as groups 17.4 group computations 17.5 determination of the groups 18 rational projective curves 18.1 the projective concept 18.2 quartics with three double points 18.3 the deficiency of a curve 18.4 some rational curves 18.5 some non-rational curves index ... |
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