Abstract
We propose the two heaviest Weierstrass n-semigroups for non- hyperelliptic curves (one on trigonal curves with maximal Maroni invariant and with totally ramification points and one on bielliptic curves and with as points some of the ramification points). We compute them when n = 2.
Highlights
We propose the two “heaviest” Weierstrass n-semigroups for nonhyperelliptic curves
We would like to find the n-semigroups with maximal weight and maximal gist among the non-hyperelliptic curves
It is better to separate the problem if we allow curves which are covering of a curve of positive genus
Summary
We propose the two “heaviest” Weierstrass n-semigroups for nonhyperelliptic curves (one on trigonal curves with maximal Maroni invariant and with totally ramification points and one on bielliptic curves and with as points some of the ramification points). We would like to find the n-semigroups with maximal weight and maximal gist (for fixed g, n) among the non-hyperelliptic curves In the second case it should be with X trigonal (see Examples 1 and 2 in which we compute H(P1, P2) and v(P1, P2)).
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