Intersection Number of Plane Curves

Intersection Number of Plane Curves

Bibliographic Details
Main Author: Nichols, Margaret E.
Language:English
Published: Oberlin College Honors Theses / OhioLINK 2013
Subjects:
Mathematics
algebraic geometry
plane curves
intersection number
Bezouts theorem
Online Access:http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1385137385
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spelling ndltd-OhioLink-oai-etd.ohiolink.edu-oberlin13851373852021-08-03T05:24:02Z Intersection Number of Plane Curves Nichols, Margaret E. Mathematics algebraic geometry plane curves intersection number Bezouts theorem In algebraic geometry, seemingly geometric problems can be solved using algebraic techniques. Some of the most basic geometric objects we can study are polynomial curves in the plane. In this paper we focus on the intersections of two curves. We address both the number of times two curves intersect at a given point, counting multiplicity (whatever that means), and the total number of intersections of the curves, again counting multiplicity. The former is known as the intersection number of the curves at the point. This concept, although geometrically motivated, can be described in algebraic terms; it is this relationship which makes it such a powerful concept. The paper concludes with an important application of the intersection number, Bezout's Theorem. This ubiquitous theorem gives a beautifully concise solution to the total number of intersections, given sufficiently nice assumptions on the curves and the ambient space. 2013-11-25 English text Oberlin College Honors Theses / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1385137385 http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1385137385 unrestricted This thesis or dissertation is protected by copyright: some rights reserved. It is licensed for use under a Creative Commons license. Specific terms and permissions are available from this document's record in the OhioLINK ETD Center.
collection NDLTD
language English
sources NDLTD
topic Mathematics
algebraic geometry
plane curves
intersection number
Bezouts theorem
spellingShingle Mathematics
algebraic geometry
plane curves
intersection number
Bezouts theorem
Nichols, Margaret E.
Intersection Number of Plane Curves
author Nichols, Margaret E.
author_facet Nichols, Margaret E.
author_sort Nichols, Margaret E.
title Intersection Number of Plane Curves
title_short Intersection Number of Plane Curves
title_full Intersection Number of Plane Curves
title_fullStr Intersection Number of Plane Curves
title_full_unstemmed Intersection Number of Plane Curves
title_sort intersection number of plane curves
publisher Oberlin College Honors Theses / OhioLINK
publishDate 2013
url http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1385137385
work_keys_str_mv AT nicholsmargarete intersectionnumberofplanecurves
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