A differential characterization of generalized Weierstraß points of a compact Riemann surface of genus \(g\geq 2\) (Q1366614)

We show that the set \(S[n]\) of the Weierstraß points of order \(n\), associated to the linear system \(|nK_S|\), where \(K_S\) is a canonical divisor on a compact Riemann surface \(S\) of genus \(g\geq 2\), coincides with the zeros of the canonical representant of the first Chern class of a holomorphic line bundle, hermitian for a metric induced by the canonical hermitian jacobian metric on \(S\). This result extends to the case of Weierstraß points associated to a complete linear system without fixed points.