On the poles of regular differentials of singular curves. (English) Zbl 0788.14020

The author considers projective, possibly singular, algebraic curves defined over a field \(k\). He studies regular differentials on such a curve and the poles of these differentials on a non-singular model of the curve. The results are applied to the study of Weierstrass points on singular curves in the case that the base field is algebraically closed, and to analyse how the Hasse-Witt invariant and the zeta-function change under desingularization in the case that the base field is perfect. The paper also contains an outline of how Weil’s approach to the Riemann-Roch theorem for function fields generalizes to curves with singularities.
Reviewer: R.Piene (Oslo)


14H20 Singularities of curves, local rings
14H55 Riemann surfaces; Weierstrass points; gap sequences
13N05 Modules of differentials
14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
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