isKnownExample -- Is L a known Weierstrass semigroup?

Usage:

b = isKnownExample L
Inputs:
- L, a list, generators of the semigroup
Outputs:
- b, a Boolean value, true if L is a known example of a Weierstrass semigroup

Description

Certain semigroups are known to be Weierstrass. For example L has 2 or 3 generators only, by work of Pinkham and Sally. Eisenbud-Harris proved that semigroups L of weight(L)<genus(L) are smoothable, and Pflueger extended this to show that semigroups L of ewt(L)<genus(L) are smoothable. Komeda proved that anysemigroup with min L < 6 is Weierstrass. In "A minimal non-Weierstrass Semigroup" by Eisenbud and Schreyer it is shown that all semigroups of genus <13 are Weierstrass but that the semigroup {6,9,13,16}, of genus 13, is not.

i1 : L={7,12,13}

o1 = {7, 12, 13}

o1 : List

i2 : isKnownExample L

o2 = true

i3 : L={7,8,9,11,13}

o3 = {7, 8, 9, 11, 13}

o3 : List

i4 : ewt L, genus L

o4 = (7, 8)

o4 : Sequence

i5 : isKnownExample L

o5 = true

i6 : LL=findSemigroups(9,10);#LL

o7 = 29

i8 : LL = flatten apply (11, g->findSemigroups g);#LL

o9 = 478

i10 : Lknown = select(LL, s -> isKnownExample s);#Lknown

o11 = 362

i12 : tally apply(Lknown, L->(
           if #L <= 3 then "Hilbert-Burch" else
           if #L == 4 and type L == 1 then "Buchsbaum-Eisenbud" else
           if weight L < genus L then "Eisenbud-Harris" else
           if ewt L < genus L then "Plueger" else
           if min L <6 then "Komeda-Low Multiplicity"))

o12 = Tally{Buchsbaum-Eisenbud => 9      }
            Eisenbud-Harris => 198
            Hilbert-Burch => 82
            Komeda-Low Multiplicity => 21
            null => 2
            Plueger => 50

o12 : Tally

Ways to use isKnownExample:

isKnownExample(List)

For the programmer

The object isKnownExample is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.06+ds/M2/Macaulay2/packages/NumericalSemigroups.m2:3204:0.

isKnownExample -- Is L a known Weierstrass semigroup?

Description

See also

Ways to use isKnownExample:

For the programmer