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Homework Statement
I am reading the undergraduate introduction to algebraic geometry entitled "Ideals, Varieties and Algorithms: An introduction to Computational Algebraic Geometry and Commutative Algebra (Third Edition) by David Cox, John Little and Donal O'Shea ... ...
I am currently focused on Chapter 8, Section 1: The Projective Plane ... ... and need help getting started with Exercises 5(a) and 5(b) ... ...Exercise 5 in Section 8.1 reads as follows:
Can someone please help me to get started on Exercises 5(a) and 5(b) shown above ...
2. Homework Equations
The definitions 1, 2 and 3 in Cox et al Section 8.1 may be relevant ... see the text provided below ...
...
The Attempt at a Solution
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I am very unsure how to start on this exercise ... but i suspect that the following transformation or map as given in Cox et al Section 8.1 directly after Definition 3 is involved:
##\mathbb{R}^2 \longrightarrow \mathbb{P}^2 ( \mathbb{R} ) ##
where ##(x, y) \in \mathbb{R}^2## is sent to the point ##p \in \mathbb{P}^2 ( \mathbb{R} )## whose homogeneous coordinates are ##(x, y, 1)##Hope someone can help ...
Peter
======================================================================To give readers of the above post some idea of the context of the exercise and also the notation I am providing some relevant text from Cox et al ... ... as follows:
Attachments
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Cox et al ... Exercise 5, Section 8.1 ... ....png15.2 KB · Views: 646
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Cox et al ...- 1 - The Projective Plane - page 1 ... ....png54.6 KB · Views: 586
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Cox et al ...- 2 - The Projective Plane - page 2 ... ....png23.8 KB · Views: 683
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Cox et al ...- 3 - The Projective Plane - page 3 ... ....png42.7 KB · Views: 625
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Cox et al ...- 4 - The Projective Plane - page 4 ... ....png37.2 KB · Views: 645
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Cox et al ...- 5 - The Projective Plane - page 5 ... ....png43.6 KB · Views: 643
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Cox et al ...- 6 - The Projective Plane - page 6 ... ....png44 KB · Views: 646
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