Theta-characteristics on curves in characteristic two
Let \textbf{L} be a family of theta-characteristics relative to f: \(U\to S\) a flat family of smooth projective curves over an algebraically closed field \({\mathbb{F}}\) of characteristic two. The author first proves that the set \(\{s\in S| \;{\mathbf{L}}| f^{-1}(s)\) is even\} is open and closed in S, which shows that we have \(e(g)\) even theta-characteristics on every ordinary smooth curve of genus \(g\) over \({\mathbb{F}}\), and secondly expressed explicitly the integer \(e(g)\) in \(g\).
scientific article; zbMATH DE number 4156635