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SpecialFanoFourfolds : Index
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ambientFivefold
-- get the ambient fivefold of the Hodge-special fourfold
ambientFivefold(HodgeSpecialFourfold)
-- get the ambient fivefold of the Hodge-special fourfold
associatedCastelnuovoSurface
-- Castelnuovo surface associated to a rational complete intersection of three quadrics in P^7
associatedCastelnuovoSurface(...,Singular=>...)
-- whether to transfer computation to Singular
associatedCastelnuovoSurface(...,Strategy=>...)
-- Castelnuovo surface associated to a rational complete intersection of three quadrics in P^7
associatedCastelnuovoSurface(...,Verbose=>...)
-- request verbose feedback
associatedCastelnuovoSurface(IntersectionOfThreeQuadricsInP7)
-- Castelnuovo surface associated to a rational complete intersection of three quadrics in P^7
associatedK3surface
-- K3 surface associated to a rational fourfold
associatedK3surface(...,Singular=>...)
-- whether to transfer computation to Singular
associatedK3surface(...,Strategy=>...)
-- K3 surface associated to a rational fourfold
associatedK3surface(...,Verbose=>...)
-- request verbose feedback
associatedK3surface(SpecialCubicFourfold)
-- K3 surface associated to a rational cubic fourfold
associatedK3surface(SpecialGushelMukaiFourfold)
-- K3 surface associated to a rational Gushel-Mukai fourfold
beauvilleMap
-- construction of Beauville for complete intersections of three quadrics in P^7
beauvilleMap(IntersectionOfThreeQuadricsInP7)
-- construction of Beauville for complete intersections of three quadrics in P^7
building
-- K3 surface associated to a rational fourfold
check(CongruenceOfCurves)
-- check that a congruence of curves is well-defined
check(ZZ,CongruenceOfCurves)
-- check that a congruence of curves is well-defined
clean(HodgeSpecialFourfold)
-- clean the internal information of a fourfold
CongruenceOfCurves
-- the class of all congruences of secant curves to surfaces
CongruenceOfCurves EmbeddedProjectiveVariety
-- get the curve of a congruence passing through a point
CongruenceOfCurves Ideal
-- get the curve of a congruence passing through a point
detectCongruence
-- detect and return a congruence of secant curves to a surface
detectCongruence(...,Verbose=>...)
-- request verbose feedback
detectCongruence(HodgeSpecialFourfold)
-- detect and return a congruence of secant curves to a surface
detectCongruence(HodgeSpecialFourfold,ZZ)
-- detect and return a congruence of secant curves to a surface
detectCongruence(SpecialCubicFourfold)
-- detect and return a congruence of (3e-1)-secant curves of degree e
detectCongruence(SpecialCubicFourfold,ZZ)
-- detect and return a congruence of (3e-1)-secant curves of degree e
detectCongruence(SpecialGushelMukaiFourfold)
-- detect and return a congruence of (2e-1)-secant curves of degree e inside a del Pezzo fivefold
detectCongruence(SpecialGushelMukaiFourfold,ZZ)
-- detect and return a congruence of (2e-1)-secant curves of degree e inside a del Pezzo fivefold
discriminant(HodgeSpecialFourfold)
-- discriminant of a special cubic fourfold
discriminant(SpecialCubicFourfold)
-- discriminant of a special cubic fourfold
discriminant(SpecialGushelMukaiFourfold)
-- discriminant of a special Gushel-Mukai fourfold
fanoFourfold
-- random prime Fano fourfold of coindex at most 3
fanoFourfold(...,CoefficientRing=>...)
-- random prime Fano fourfold of coindex at most 3
fanoFourfold(ZZ,ZZ)
-- random prime Fano fourfold of coindex at most 3
fromOrdinaryToGushel
-- try to deform to a fourfold of Gushel type
fromOrdinaryToGushel(SpecialGushelMukaiFourfold)
-- try to deform to a fourfold of Gushel type
GMtables
-- make examples of reducible subschemes of P^5
GMtables(...,Verify=>...)
-- make examples of reducible subschemes of P^5
GMtables(ZZ)
-- make examples of reducible subschemes of P^5
GMtables(ZZ,Ring)
-- make examples of reducible subschemes of P^5
HodgeSpecialFourfold
-- the class of all Hodge-special fourfolds
IntersectionOfThreeQuadricsInP7
-- the class of all special intersection of three quadrics in P^7
isAdmissible
-- whether an integer is admissible (in the sense of the theory of cubic fourfolds)
isAdmissible(SpecialCubicFourfold)
-- whether an integer is admissible (in the sense of the theory of cubic fourfolds)
isAdmissible(ZZ)
-- whether an integer is admissible (in the sense of the theory of cubic fourfolds)
isAdmissibleGM
-- whether an integer is admissible (in the sense of the theory of GM fourfolds)
isAdmissibleGM(SpecialGushelMukaiFourfold)
-- whether an integer is admissible (in the sense of the theory of GM fourfolds)
isAdmissibleGM(ZZ)
-- whether an integer is admissible (in the sense of the theory of GM fourfolds)
isMember(EmbeddedProjectiveVariety,CongruenceOfCurves)
-- test membership in a congruence of curves
map(CongruenceOfCurves)
-- compute the parameter space of a congruence
map(SpecialCubicFourfold)
-- associated cubic map
map(SpecialGushelMukaiFourfold)
-- associated quadratic map
mirrorFourfold
-- associated fourfold to a rational cubic or GM fourfold
mirrorFourfold(...,Singular=>...)
-- whether to transfer computation to Singular
mirrorFourfold(...,Strategy=>...)
-- associated fourfold to a rational cubic or GM fourfold
mirrorFourfold(...,Verbose=>...)
-- request verbose feedback
mirrorFourfold(HodgeSpecialFourfold)
-- associated fourfold to a rational cubic or GM fourfold
mirrorFourfold(IntersectionOfThreeQuadricsInP7)
-- associated fourfold to a rational cubic or GM fourfold
mirrorFourfold(SpecialCubicFourfold)
-- associated fourfold to a rational cubic or GM fourfold
mirrorFourfold(SpecialGushelMukaiFourfold)
-- associated fourfold to a rational cubic or GM fourfold
normalSheaf
-- normal sheaf
normalSheaf(EmbeddedProjectiveVariety)
-- normal sheaf
normalSheaf(EmbeddedProjectiveVariety,EmbeddedProjectiveVariety)
-- normal sheaf
parameterCount
-- count of parameters
parameterCount(...,Verbose=>...)
-- request verbose feedback
parameterCount(EmbeddedProjectiveVariety,EmbeddedProjectiveVariety)
-- count of parameters
parameterCount(HodgeSpecialFourfold)
-- count of parameters
parameterCount(SpecialCubicFourfold)
-- count of parameters in the moduli space of GM fourfolds
parameterCount(SpecialGushelMukaiFourfold)
-- count of parameters in the moduli space of GM fourfolds
parametrize(HodgeSpecialFourfold)
-- rational parametrization
parametrizeFanoFourfold
-- rational parametrization of a prime Fano fourfold of coindex at most 3
parametrizeFanoFourfold(...,Strategy=>...)
-- rational parametrization of a prime Fano fourfold of coindex at most 3
parametrizeFanoFourfold(EmbeddedProjectiveVariety)
-- rational parametrization of a prime Fano fourfold of coindex at most 3
Singular
-- whether to transfer computation to Singular
SpecialCubicFourfold
-- the class of all special cubic fourfolds
specialCubicFourfold
-- make a special cubic fourfold
specialCubicFourfold(...,InputCheck=>...)
-- make a special cubic fourfold
specialCubicFourfold(...,NumNodes=>...)
-- make a special cubic fourfold
specialCubicFourfold(...,Verbose=>...)
-- request verbose feedback
specialCubicFourfold(EmbeddedProjectiveVariety)
-- random special cubic fourfold
specialCubicFourfold(EmbeddedProjectiveVariety,EmbeddedProjectiveVariety)
-- make a special cubic fourfold
specialCubicFourfold(Ideal)
-- random special cubic fourfold
specialCubicFourfold(Ideal,Ideal)
-- make a special cubic fourfold
specialCubicFourfold(Ideal,RingElement)
-- make a special cubic fourfold
specialCubicFourfold(String)
-- random special cubic fourfold of a given type
specialCubicFourfold(String,Ring)
-- random special cubic fourfold of a given type
SpecialFanoFourfolds
-- A package for working with Hodge-special fourfolds
specialFourfold
-- make a Hodge-special fourfold
specialFourfold(...,InputCheck=>...)
-- make a Hodge-special fourfold
specialFourfold(...,NumNodes=>...)
-- make a Hodge-special fourfold
specialFourfold(...,Verbose=>...)
-- request verbose feedback
specialFourfold(EmbeddedProjectiveVariety)
-- make a Hodge-special fourfold
specialFourfold(EmbeddedProjectiveVariety,EmbeddedProjectiveVariety)
-- make a Hodge-special fourfold
specialFourfold(EmbeddedProjectiveVariety,EmbeddedProjectiveVariety,EmbeddedProjectiveVariety)
-- make a Hodge-special fourfold
specialFourfold(Ideal)
-- make a Hodge-special fourfold
specialFourfold(Ideal,Ideal)
-- make a Hodge-special fourfold
specialFourfold(Ideal,RingElement)
-- make a Hodge-special fourfold
specialFourfold(String)
-- make a Hodge-special fourfold
specialFourfold(String,Ring)
-- make a Hodge-special fourfold
specialFourfold(String,ZZ)
-- load a prebuilt example of fourfold
SpecialGushelMukaiFourfold
-- the class of all special Gushel-Mukai fourfolds
specialGushelMukaiFourfold
-- make a special Gushel-Mukai fourfold
specialGushelMukaiFourfold(...,InputCheck=>...)
-- make a special Gushel-Mukai fourfold
specialGushelMukaiFourfold(...,Verbose=>...)
-- request verbose feedback
specialGushelMukaiFourfold(Array,Array)
-- construct GM fourfolds by gluing cubic or quartic scrolls to surfaces in PP^6
specialGushelMukaiFourfold(Array,Array,String)
-- construct GM fourfolds by gluing cubic or quartic scrolls to surfaces in PP^6
specialGushelMukaiFourfold(Array,Array,String,Thing)
-- construct GM fourfolds by gluing cubic or quartic scrolls to surfaces in PP^6
specialGushelMukaiFourfold(Array,Array,Thing)
-- construct GM fourfolds by gluing cubic or quartic scrolls to surfaces in PP^6
specialGushelMukaiFourfold(EmbeddedProjectiveVariety)
-- random special Gushel-Mukai fourfold
specialGushelMukaiFourfold(EmbeddedProjectiveVariety,EmbeddedProjectiveVariety)
-- make a special Gushel-Mukai fourfold
specialGushelMukaiFourfold(Ideal)
-- random special Gushel-Mukai fourfold
specialGushelMukaiFourfold(Ideal,Ideal)
-- make a special Gushel-Mukai fourfold
specialGushelMukaiFourfold(String)
-- random special Gushel-Mukai fourfold of a given type
specialGushelMukaiFourfold(String,Ring)
-- random special Gushel-Mukai fourfold of a given type
surface
-- get the special surface contained in the fourfold
surface(HodgeSpecialFourfold)
-- get the special surface contained in the fourfold
surface(List)
-- get a rational surface
surface(MultiprojectiveVariety,MultiprojectiveVariety)
-- make a Hodge-special surface
surface(VisibleList,Option)
-- get a rational surface
surface(VisibleList,Option,Option)
-- get a rational surface
surface(VisibleList,Ring)
-- get a rational surface
surface(VisibleList,Ring,Option)
-- get a rational surface
surface(VisibleList,Ring,Option,Option)
-- get a rational surface
toExternalString(HodgeSpecialFourfold)
-- convert to a readable string
toGrass
-- Gushel morphism from a GM fourfold to GG(1,4)
toGrass(EmbeddedProjectiveVariety)
-- embedding of an ordinary Gushel-Mukai fourfold or a del Pezzo variety into GG(1,4)
toGrass(SpecialGushelMukaiFourfold)
-- Gushel morphism from a GM fourfold to GG(1,4)
trisecantFlop
-- examples of trisecant flops
trisecantFlop(...,Verbose=>...)
-- request verbose feedback
unirationalParametrization
-- unirational parametrization
unirationalParametrization(HodgeSpecialFourfold)
-- unirational parametrization
unirationalParametrization(SpecialCubicFourfold)
-- unirational parametrization
unirationalParametrization(SpecialCubicFourfold,EmbeddedProjectiveVariety)
-- unirational parametrization
unirationalParametrization(SpecialGushelMukaiFourfold)
-- unirational parametrization
Verbose
-- request verbose feedback