Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1 by Elena Guardo & Adam Van Tuyl

Author:Elena Guardo & Adam Van Tuyl
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

with and . By Lemma 5.1, Y is a complete intersection. Furthermore, if we set and , then again by Lemma 5.1 we have

where and . (Recall that v = α 1.)

Let . Because , it follows that . Hence, since . We now prove the following claim.

Claim.

.

Proof of the Claim.

By construction, , and thus . Hence, we want to show that .

So, if , then there is an and an H 2 ∈ R such that . Because F, G ∈ I(Y ) and , so we have .

To show the reverse inclusion, let . Since K ∈ I(Y ), there exist H 1, H 2 ∈ R such that It now suffices to show that . Take any point . By construction, A ≠ A i for . Now

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.