Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
2.11. Let f e r(V), V a variety c A". Define 1 G(f) = {(a1,..., An, An+1) € A"+ |(a1,..., an) E V and an+1 = f(aj,..., an)}, the graph of f. Show that G(f) is an affine variety, and that the map (a1,..., an) - (a1,..., an, f (a1,..., an)) defines an isomorphism of V with G(f). (Projection gives the inverse.)

2.11. Let f e r(V), V a variety c A". Define 1 G(f) = {(a1,..., An, An+1) € A"+ |(a1,..., an) E V and an+1 = f(aj,..., an)}, the graph of f. Show that G(f) is an affine variety, and that the map (a1,..., an) - (a1,..., an, f (a1,..., an)) defines an isomorphism of V with G(f). (Projection gives the inverse.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
1
2.11. Let f e r(V), V a variety cA". Define G(f) = {(a1,….., An, An+1) E A"*' |(a1,..., an) E V and an+1 = f(a1,..., An)}, the graph of f. Show that G(f) is an affine variety, and that the map (a1,..., an) – (a1,..., an, f(a1,..., an)) defines an isomorphism of V with G(f). (Projection gives the inverse.)
Transcribed Image Text:2.11. Let f e r(V), V a variety cA". Define G(f) = {(a1,….., An, An+1) E A"*' |(a1,..., an) E V and an+1 = f(a1,..., An)}, the graph of f. Show that G(f) is an affine variety, and that the map (a1,..., an) – (a1,..., an, f(a1,..., an)) defines an isomorphism of V with G(f). (Projection gives the inverse.)
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS