buchweitz -- An example of a semigroup that is not a Weierstrass semigroup

For i>=0 this produces a semigroup B with genus 16+i, conductor 26+2i, and #sums(2, gaps buchweitz i) = 3*(genus B -1)+1). This implies that these semigroups are NOT Weierstrass semigroups by the following argument, first employed by Buchweitz:

If L generates the Weierstrass semigroup of a point x on a Riemann surface C, then the gaps L is the set {1+v | v is the order at p of vanishing of a global section of \omega_C}. Thus sums(d, #gaps L) <= dim H^0(\omega_C^{d) = d*(2g-1) - g + 1.

More such semigroups can be found with buchweitzSemigroups

The result was written in Ragnar Buchweitz' These d'Etat, but never otherwise published by Buchweitz. In the meantime it became famous anyway.