I'm reading the following article by Mumford speaking about theta characteristic. Mumford's article
I'm trying to understand the definition af the quadric form $q$ on page 184.
Here my questions:
1) In your opinion what does it mean that $a_i \in E(a)_{p_i}$ define, for $i$ from 1 to $N$, the section $\overline{a} \in E(a)/E(-a)$?
2) How is $Q$ extended to a quadratic map $E(a) \rightarrow \Omega^{1}_{X}(2a)$?
Thanks in advance for any suggestions.