Plane Algebraic Curves

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Birkhäuser, 11.11.2013 - 721 Seiten
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Inhalt

History of algebraic curves
1
The cissoid of Diocles
9
The spiric sections of Perseus
16
Caustics and contour curves in optics and perspective
41
Further examples of curves from science
58
Synthetic and analytic geometry
66
Examples of the application of analytic methods
79
Newtons investigation of cubic curves
87
Cubics elliptic curves and abelian varieties
306
Investigation of curves by resolution
323
Singularities as analytic set germs
337
Newton polygons and Puiseux expansions
370
66
374
Resolution of singularities by quadratic
455
Topology of singularities
535
Global investigations
575

Descriptive geometry and projective geometry
102
The projective plane as a manifold
118
Complex projective geometry
136
Investigation of curves by elementary algebraic methods
172
Zeroes of polynomials
190
The intersection of plane curves
227
The intersection ring of P2
260
Some simple types of curves
278
The formulae of Clebsch and Noether
601
Differential forms on Riemann surfaces
627
Bibliography
694
69
697
87
704
306
708
172
716
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