Level n-structure as defined by Mumford in GIT - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T06:04:43Z http://mathoverflow.net/feeds/question/90729 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/90729/level-n-structure-as-defined-by-mumford-in-git Level n-structure as defined by Mumford in GIT rghthndsd 2012-03-09T16:38:23Z 2012-03-09T16:38:23Z <p>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) $n_A \circ \sigma_i= \varepsilon$.</p> <p>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.</p>