Lemma 31.14.2 (0B3P)—The Stacks project

Loading web-font TeX/Math/Italic

Table of contents
Part 2: Schemes
Chapter 31: Divisors
Section 31.14: Effective Cartier divisors and invertible sheaves
Lemma 31.14.2 (cite)

previous definition
next lemma

numberstags

history
statistics
3 tags refer to this tag

Lemma 31.14.2. Let $S$ be a scheme and let $D \subset S$ be an effective Cartier divisor. Then the conormal sheaf is $\mathcal{C}_{D/S} = \mathcal{I}_ D|_ D = \mathcal{O}_ S(-D)|_ D$ and the normal sheaf is $\mathcal{N}_{D/S} = \mathcal{O}_ S(D)|_ D$ .

Proof. This follows from Morphisms, Lemma 29.31.2. $\square$

Comments (0)

There are also:

2 comment(s) on Section 31.14: Effective Cartier divisors and invertible sheaves

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$ ). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Comments (0)

Post a comment