Math 480, Spring 2014, Assignment 10

Carefully define the following terms:

1. Irrelevant ideal.

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

1. Theorem on descending chains of projective varieties (Theorem 6(i) in section 8.3 of the text).
2. Theorem on irreducible decomposition of projective varieties (Theorem 6(ii) in section 8.3).
3. Theorem on radicals of homogeneous ideals (Proposition 7 in section 8.3).
4. Projective weak Nullstellensatz.
5. Projective strong Nullstellensatz.
6. Projective algebra-geometry dictionary (Theorem 10 in section 8.3).

Solve the following problems:

1. Section 8.3, problem 7.

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