Abstract
The complex projective plane is the natural efficient context where to study algebraic curves: curves whose equation is polynomial. We study the questions of tangency, singularity, multiplicity, inflexion points. We investigate the number of intersection points of two curves and prove various versions of the corresponding Bezout theorem. We pay special attention to the cubics, the properties of their inflexion points and the abelian group attached to them. We also investigate the rational curves: those admitting parametric equations in terms of rational fractions.
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References and Further Reading
F. Borceux, A Differential Approach to Geometry, Geometric Trilogy III (Springer, Berlin, 2014)
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© 2014 Springer International Publishing Switzerland
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Borceux, F. (2014). Algebraic Curves. In: An Algebraic Approach to Geometry. Springer, Cham. https://doi.org/10.1007/978-3-319-01733-4_7
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DOI: https://doi.org/10.1007/978-3-319-01733-4_7
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-01732-7
Online ISBN: 978-3-319-01733-4
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