First vertices for generic Newton polygons, and $p$-cyclic coverings of the projective line

Details First vertices for generic Newton polygons, and $p$-cyclic coverings of the projective line First vertices for generic Newton polygons, and $p$-cyclic coverings of the projective line

2009-12-10

arxiv.org/abs/0912.2051v1

Mathematics

Algebraic Geometry

partial results, comments welcome

Scientific paper

In this paper we compute the first vertex of a generic Newton polygon in some
special cases, and the corresponding Hasse polynomial. This allows us to show
the nonexistence of $p$-cyclic coverings of the projective line in
characteristic $p$ with supersingular jacobian for some (infinite families of)
genera.

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