An Example!

Algebraic Geometry
Post Reply
Tsakanikas Nickos
Community Team
Posts: 314
Joined: Tue Nov 10, 2015 8:25 pm

An Example!

#1

Post by Tsakanikas Nickos »

Consider the ring homomorphism
\[ \phi \ \colon \mathbb{C}[x,y] \longrightarrow \mathbb{C}[s,t] \\
x \mapsto s \\
y \mapsto st \]and the induced morphism of affine schemes \[ f \ \colon \mathbb{A}^{2}_{\mathbb{C}} = \text{Spec}\ \mathbb{C}[s,t] \longrightarrow \mathbb{A}^{2}_{\mathbb{C}} = \text{Spec} \ \mathbb{C}[x,y] \] Describe the pre-image $ f^{-1}(\mathfrak{m}) $ of the maximal ideal $ \mathfrak{m} = (x-a,y-b) \subset \mathbb{C}[x,y] $, where $ a,b \in \mathbb{C} $. View this result from a geometrical approach (with points in $\mathbb{C}^{2}$).
Post Reply

Create an account or sign in to join the discussion

You need to be a member in order to post a reply

Create an account

Not a member? register to join our community
Members can start their own topics & subscribe to topics
It’s free and only takes a minute

Register

Sign in

Who is online

Users browsing this forum: No registered users and 9 guests