MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

In Mumford's GIT, the definition of level $n$ structure ($n \geq 2)$ is $2g$ sections $\{\sigma_1, \dots, \sigma_{2g}\} : S \rightarrow A$ such that two conditions hold: (i) For geometric points the sections form a basis for the $n$-torsion points and (ii) $n_A \circ \sigma_i= \varepsilon$.

My question is: Doesn't (i) imply (ii)? Corollary 6.2 implies that since the two maps are equal on geometric fibers by (i), they must be equal everywhere.

share|cite|improve this question

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.