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SpecialFanoFourfolds : Table of Contents
SpecialFanoFourfolds
-- A package for working with Hodge-special fourfolds
ambientFivefold
-- get the ambient fivefold of the Hodge-special fourfold
associatedCastelnuovoSurface
-- Castelnuovo surface associated to a rational complete intersection of three quadrics in P^7
associatedK3surface
-- K3 surface associated to a rational fourfold
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
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
detectCongruence
-- detect and return a congruence of secant curves to a surface
detectCongruence(SpecialCubicFourfold,ZZ)
-- detect and return a congruence of (3e-1)-secant curves of degree e
detectCongruence(SpecialGushelMukaiFourfold,ZZ)
-- detect and return a congruence of (2e-1)-secant curves of degree e inside a del Pezzo fivefold
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
fromOrdinaryToGushel
-- try to deform to a fourfold of Gushel type
GMtables
-- 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)
isAdmissibleGM
-- 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
normalSheaf
-- normal sheaf
parameterCount
-- 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
Singular
-- whether to transfer computation to Singular
SpecialCubicFourfold
-- the class of all special cubic fourfolds
specialCubicFourfold
-- make a special cubic fourfold
specialCubicFourfold(EmbeddedProjectiveVariety)
-- random special cubic fourfold
specialCubicFourfold(String,Ring)
-- random special cubic fourfold of a given type
specialFourfold
-- 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(Array,Array,String,Thing)
-- construct GM fourfolds by gluing cubic or quartic scrolls to surfaces in PP^6
specialGushelMukaiFourfold(EmbeddedProjectiveVariety)
-- random special Gushel-Mukai fourfold
specialGushelMukaiFourfold(String,Ring)
-- random special Gushel-Mukai fourfold of a given type
surface
-- get the special surface contained in the fourfold
surface(List)
-- get a rational surface
surface(MultiprojectiveVariety,MultiprojectiveVariety)
-- make a Hodge-special 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)
trisecantFlop
-- examples of trisecant flops
unirationalParametrization
-- unirational parametrization
Verbose
-- request verbose feedback