Serre, Jean-Pierre Coverings with odd ramification and theta-characteristics. (Revêtements à ramification impaire et thêta-caractéristiques.) (French) Zbl 0742.14030 C. R. Acad. Sci., Paris, Sér. I 311, No. 9, 547-552 (1990). Author’s abstract: “Let \(\pi:X\to Y\) be a ramified covering of compact Riemann surfaces; assume that all the ramification degrees of \(\pi\) are odd. We define some invariants of \(\pi\), belonging to \(H^ i(X,\mathbb{Z}/2\mathbb{Z})\) for \(i=1,2\), and we prove some relations between them. If \(c\) is a theta-characteristic of \(X\), there is a corresponding theta- characteristic \(\pi'c\) of \(Y\), and we show how to compute the parity of \(\pi'c\) from that of \(c\), using the invariants defined above”. Reviewer: V.Z.Enol’skij (Kiev) Cited in 5 ReviewsCited in 13 Documents MSC: 14H55 Riemann surfaces; Weierstrass points; gap sequences 14H30 Coverings of curves, fundamental group 30F10 Compact Riemann surfaces and uniformization 14H42 Theta functions and curves; Schottky problem Keywords:ramified covering of compact Riemann surfaces; theta-characteristic PDFBibTeX XMLCite \textit{J.-P. Serre}, C. R. Acad. Sci., Paris, Sér. I 311, No. 9, 547--552 (1990; Zbl 0742.14030)