Abstract
A point on an algebraic curve is either “simple” or “singular.” At a simple point the curve is “smooth.” In general,a point on a curve is assigned a “multiplicity” that indicates how many times it has to be counted as a point of the curve. The “tangents” of a curve will also be explained.One can decide whether a point is simple or singular with the help of the local ring at the point.The facts from Appendix E on Noetherian rings and discrete valuation rings will play a role in this chapter.Toward the end, some theorems from Appendix F on integral ring extensions wil l al so be needed.
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© 2005 Birkhäuser Boston
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(2005). Regular and Singular Points of Algebraic Curves. Tangents. In: Introduction to Plane Algebraic Curves. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4443-1_6
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DOI: https://doi.org/10.1007/0-8176-4443-1_6
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4381-2
Online ISBN: 978-0-8176-4443-7
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