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