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Coverings with odd ramification and theta-characteristics. (Revêtements à ramification impaire et thêta-caractéristiques.) (French) Zbl 0742.14030

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”.

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
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