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SpecialFanoFourfolds :: SpecialFanoFourfolds

SpecialFanoFourfolds -- A package for working with special cubic fourfolds and special Gushel-Mukai fourfolds

Description

This package depends on the following other Macaulay2 packages: Cremona, RationalMaps, CharacteristicClasses, Resultants.

Author

Version

This documentation describes version 1.0 of SpecialFanoFourfolds.

Source code

The source code from which this documentation is derived is in the file SpecialFanoFourfolds.m2.

Exports

  • Types
  • Functions and commands
  • Methods
    • < SpecialGushelMukaiFourfold -- try to deform to a fourfold of Gushel type
    • "associatedK3surface(SpecialCubicFourfold)" -- see associatedK3surface -- associated K3 surface to a rational cubic fourfold
    • "associatedK3surface(SpecialGushelMukaiFourfold)" -- see associatedK3surface -- associated K3 surface to a rational cubic fourfold
    • "coneOfLines(Ideal,Ideal)" -- see coneOfLines -- cone of lines on a subvariety passing through a point
    • "cycleClass(Ideal)" -- see cycleClass -- determine the expression of the class of a cycle as a linear combination of Schubert classes
    • "detectCongruence(SpecialCubicFourfold)" -- see detectCongruence -- detect and return a congruence of (3e-1)-secant curves of degree e
    • "detectCongruence(SpecialCubicFourfold,ZZ)" -- see detectCongruence -- detect and return a congruence of (3e-1)-secant curves of degree e
    • "detectCongruence(SpecialGushelMukaiFourfold)" -- see detectCongruence -- detect and return a congruence of (3e-1)-secant curves of degree e
    • "detectCongruence(SpecialGushelMukaiFourfold,ZZ)" -- see detectCongruence -- detect and return a congruence of (3e-1)-secant curves of degree e
    • "fanoFourfold(ZZ,ZZ)" -- see fanoFourfold -- random prime Fano fourfold of coindex at most 3
    • "grassmannianHull(SpecialGushelMukaiFourfold)" -- see grassmannianHull -- grassmannian hull of a Gushel-Mukai fourfold
    • ideal(SpecialCubicFourfold) -- ideal of the fourfold
    • "ideal(SpecialGushelMukaiFourfold)" -- see ideal(SpecialCubicFourfold) -- ideal of the fourfold
    • "ideals(SpecialCubicFourfold)" -- see ideals -- corresponding ideals
    • "ideals(SpecialGushelMukaiFourfold)" -- see ideals -- corresponding ideals
    • "isAdmissible(SpecialCubicFourfold)" -- see isAdmissible -- whether an integer is admissible (in the sense of the theory of cubic fourfolds)
    • "isAdmissible(ZZ)" -- see isAdmissible -- whether an integer is admissible (in the sense of the theory of cubic fourfolds)
    • "isAdmissibleGM(SpecialGushelMukaiFourfold)" -- see isAdmissibleGM -- whether an integer is admissible (in the sense of the theory of GM fourfolds)
    • "isAdmissibleGM(ZZ)" -- see isAdmissibleGM -- whether an integer is admissible (in the sense of the theory of GM fourfolds)
    • map(SpecialCubicFourfold) -- associated cubic map
    • map(SpecialGushelMukaiFourfold) -- associated quadratic map
    • "normalSheaf(Ideal)" -- see normalSheaf -- normal sheaf
    • "normalSheaf(Ideal,Ideal)" -- see normalSheaf -- normal sheaf
    • "parameterCount(Ideal,Ideal)" -- see parameterCount -- count of parameters
    • "parameterCount(SpecialCubicFourfold)" -- see parameterCount -- count of parameters
    • parameterCount(SpecialGushelMukaiFourfold) -- count of parameters in the moduli space of GM fourfolds
    • parametrize(SpecialCubicFourfold) -- rational parametrization
    • "parametrize(SpecialGushelMukaiFourfold)" -- see parametrize(SpecialCubicFourfold) -- rational parametrization
    • "parametrizeFanoFourfold(Ideal)" -- see parametrizeFanoFourfold -- rational parametrization of a prime Fano fourfold of coindex at most 3
    • "parametrizeFanoFourfold(QuotientRing)" -- see parametrizeFanoFourfold -- rational parametrization of a prime Fano fourfold of coindex at most 3
    • ring(SpecialCubicFourfold) -- ambient polynomial ring of the fourfold
    • "ring(SpecialGushelMukaiFourfold)" -- see ring(SpecialCubicFourfold) -- ambient polynomial ring of the fourfold
    • "schubertCycle(VisibleList,Ring)" -- see schubertCycle -- take a random Schubert cycle
    • "schubertCycle(VisibleList,Ring,String)" -- see schubertCycle -- take a random Schubert cycle
    • "specialCubicFourfold(Ideal,Ideal)" -- see specialCubicFourfold -- make a special cubic fourfold
    • "specialCubicFourfold(Ideal,RingElement)" -- see specialCubicFourfold -- make a special cubic fourfold
    • specialCubicFourfold(Ideal) -- random special cubic fourfold
    • "specialCubicFourfold(String)" -- see specialCubicFourfold(Ideal) -- random special cubic fourfold
    • "specialCubicFourfold(String,Ring)" -- see specialCubicFourfold(Ideal) -- random special cubic fourfold
    • "specialGushelMukaiFourfold(Ideal,Ideal)" -- see specialGushelMukaiFourfold -- make a special Gushel-Mukai fourfold
    • specialGushelMukaiFourfold(Ideal) -- random special Gushel-Mukai fourfold
    • "specialGushelMukaiFourfold(String)" -- see specialGushelMukaiFourfold(Ideal) -- random special Gushel-Mukai fourfold
    • "specialGushelMukaiFourfold(String,Ring)" -- see specialGushelMukaiFourfold(Ideal) -- random special Gushel-Mukai fourfold
    • "tables(ZZ)" -- see tables -- make examples of reducible subschemes of P^5
    • "tables(ZZ,Nothing)" -- see tables -- make examples of reducible subschemes of P^5
    • "tables(ZZ,Ring)" -- see tables -- make examples of reducible subschemes of P^5
    • "tables(ZZ,Ring,Nothing)" -- see tables -- make examples of reducible subschemes of P^5
    • "toGrass(SpecialGushelMukaiFourfold)" -- see toGrass -- Gushel morphism from a GM fourfold to Grass(1,4)
    • toGrass(Ideal) -- embedding of an ordinary Gushel-Mukai fourfold or a del Pezzo variety into Grass(1,4)
    • "unirationalParametrization(SpecialCubicFourfold)" -- see unirationalParametrization -- unirational parametrization
    • "unirationalParametrization(SpecialCubicFourfold,Ideal)" -- see unirationalParametrization -- unirational parametrization
    • "unirationalParametrization(SpecialGushelMukaiFourfold)" -- see unirationalParametrization -- unirational parametrization
  • Symbols

For the programmer

The object SpecialFanoFourfolds is a package.