Math 480, Spring 2014, Assignment 1

Carefully define the following terms, then give one example and one non-example of each:

1. Regular map (from one affine algebraic variety to another).
2. Regular function.
3. The coordinate ring $\mathsf{k}[V]$ of a variety $V$.
4. Isomorphism (from one variety to another).

Carefully state the following theorems (you need not prove them):

1. Theorem relating irreducibility of $V$ to zero-divisors in $\mathsf{k}[V]$.

Solve the following problems:

1. Section 5.1, problems 1, 2, 4, and 6.

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