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(CubicFourfold) -- K3 surface associated to a rational cubic fourfold
• associatedK3surface(GushelMukaiFourfold) -- 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
• CubicFourfold -- the class of all special cubic fourfolds
• cubicFourfold -- make a special cubic fourfold
• cubicFourfold(EmbeddedProjectiveVariety) -- random special cubic fourfold
• cubicFourfold(String,Ring) -- random special cubic fourfold of a given type
• detectCongruence -- detect and return a congruence of secant curves to a surface
• detectCongruence(CubicFourfold,ZZ) -- detect and return a congruence of (3e-1)-secant curves of degree e
• detectCongruence(GushelMukaiFourfold,ZZ) -- detect and return a congruence of (2e-1)-secant curves of degree e inside a del Pezzo fivefold
• discriminant(CubicFourfold) -- discriminant of a special cubic fourfold
• discriminant(GushelMukaiFourfold) -- discriminant of a special Gushel-Mukai fourfold
• DoublySpecialCubicFourfold -- the class of all cubic fourfolds belonging to the intersection of two Hassett divisors
• 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
• GushelMukaiFourfold -- the class of all special Gushel-Mukai fourfolds
• gushelMukaiFourfold -- make a special Gushel-Mukai fourfold
• gushelMukaiFourfold(Array,Array,String,Thing) -- construct GM fourfolds by gluing cubic or quartic scrolls to surfaces in PP^6
• gushelMukaiFourfold(EmbeddedProjectiveVariety) -- random special Gushel-Mukai fourfold
• gushelMukaiFourfold(String,Ring) -- random special Gushel-Mukai fourfold of a given type
• 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(CubicFourfold) -- associated cubic map
• map(GushelMukaiFourfold) -- associated quadratic map
• mirrorFourfold -- associated fourfold to a rational cubic or GM fourfold
• normalSheaf -- normal sheaf
• parameterCount -- count of parameters
• parameterCount(CubicFourfold) -- count of parameters in the moduli space of GM fourfolds
• parameterCount(GushelMukaiFourfold) -- 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
• polarizedK3surface -- polarized K3 surface associated to a doubly special cubic fourfold
• Singular -- whether to transfer computation to Singular
• specialFourfold -- make a Hodge-special fourfold
• specialFourfold(String,ZZ) -- load a prebuilt example of fourfold
• surface -- get the special surface contained in the fourfold
• surface(List) -- get a rational surface
• surface(MultiprojectiveVariety,MultiprojectiveVariety) -- make a Hodge-special surface
• surfaces -- get the special surfaces contained in the cubic fourfold
• swap -- swap the order of the two special surfaces
• 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