Plane Quartics

• Invariants
  • DixmierOhnoInvariants(C): Crv → SeqEnum, SeqEnum
  • DixmierOhnoInvariants(f): RngMPolElt → SeqEnum, SeqEnum
  • Example: Dixmier-Ohno Invariants of the Klein Quartic
  • DiscriminantOfTernaryQuartic(f): RngMPolElt → Any
  • Example: Discriminant of the Klein Quartic
  • DiscriminantFromDixmierOhnoInvariants(DO): SeqEnum → Any
  • DixmierOhnoInvariantsEqual(DO1, DO2): SeqEnum, SeqEnum → BoolElt
  • DixmierOhnoAlgebraicRelations(DOinv): SeqEnum → SeqEnum
  • CovariantHessian(Phi): RngMPolElt → RngMPolElt
  • ContravariantSigmaAndPsi(Phi): RngMPolElt → RngMPolElt, RngMPolElt
  • QuarticCovariantsAndContravariants(Phi): RngMPolElt → SeqEnum
• Creation from Invariants
  • PlaneQuarticFromDixmierOhnoInvariants(DO): SeqEnum → Crv, SeqEnum
  • TernaryQuarticFromDixmierOhnoInvariants(DO): SeqEnum → RngMPolElt, SeqEnum
  • Example: Quartic from Dixmier-Ohno Invariants
• Isomorphisms
  • IsIsomorphicPlaneQuartics(X1, X2): CrvPln, CrvPln → BoolElt, SeqEnum
  • IsIsomorphicTernaryQuartics(f1, f2): RngMPolElt, RngMPolElt → BoolElt, SeqEnum
  • IsomorphismsOfPlaneQuartics(X1, X2): CrvPln, CrvPln → SeqEnum
  • IsomorphismsOfTernaryQuartics(f1, f2): RngMPolElt, RngMPolElt → SeqEnum
  • AutomorphismsOfPlaneQuartic(X): CrvPln → SeqEnum
  • AutomorphismsOfTernaryQuartic(f): RngMPolElt → SeqEnum
  • AutomorphismGroupOfPlaneQuartic(X): CrvPln → GrpPerm, Map
  • AutomorphismGroupOfTernaryQuartic(f): RngMPolElt → GrpPerm, Map
  • Example: Automorphisms of the Klein Quartic
  • AutomorphismGroupOfPlaneQuartic(X, Autos): CrvPln, SeqEnum → GrpPerm, Map
  • AutomorphismGroupOfTernaryQuartic(f, Autos): RngMPolElt, SeqEnum → GrpPerm, Map
  • GeometricAutomorphismGroup(C): Crv → GrpPerm
• Twists
  • TwistsOfPlaneQuartic(C, Autos): Crv, SeqEnum → SeqEnum[Crv], GrpPerm
  • Twists(C): Crv → SeqEnum, GrpPerm
  • Example: Twists of the Klein Quartic
• Bibliography