Lesson plan
Regular embedding
In algebraic geometry, a closed immersion i: X \hookrightarrow Y of schemes is a regular embedding of codimension r if each point x in X has an open affine neighborhood U in Y such that the ideal of X \cap U is generated by a regular sequence of length r. A regular embedding of codimension one is precisely an effective Cartier divisor.
Article summary
In algebraic geometry, a closed immersion i: X \hookrightarrow Y of schemes is a regular embedding of codimension r if each point x in X has an open affine neighborhood U in Y such that the ideal of X \cap U is generated by a regular sequence of length r. A regular embedding of codimension one is precisely an effective Cartier divisor.
Key claims
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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