HodgeSpecialFourfold -- the class of all Hodge-special fourfolds

Types of Hodge-special fourfold :

• IntersectionOfThreeQuadricsInP7 -- the class of all special intersection of three quadrics in P^7
• SpecialCubicFourfold -- the class of all special cubic fourfolds
• SpecialGushelMukaiFourfold -- the class of all special Gushel-Mukai fourfolds

Functions and methods returning a Hodge-special fourfold :

• mirrorFourfold -- associated fourfold to a rational cubic or GM fourfold
• specialFourfold -- make a Hodge-special fourfold

Methods that use a Hodge-special fourfold :

• ambientFivefold(HodgeSpecialFourfold) -- see ambientFivefold -- get the ambient fivefold of the Hodge-special fourfold
• clean(HodgeSpecialFourfold) -- clean the internal information of a fourfold
• detectCongruence(HodgeSpecialFourfold) -- see detectCongruence -- detect and return a congruence of secant curves to a surface
• detectCongruence(HodgeSpecialFourfold,ZZ) -- see detectCongruence -- detect and return a congruence of secant curves to a surface
• discriminant(HodgeSpecialFourfold) -- see discriminant(SpecialCubicFourfold) -- discriminant of a special cubic fourfold
• mirrorFourfold(HodgeSpecialFourfold) -- see mirrorFourfold -- associated fourfold to a rational cubic or GM fourfold
• parameterCount(HodgeSpecialFourfold) -- see parameterCount -- count of parameters
• parametrize(HodgeSpecialFourfold) -- rational parametrization
• surface(HodgeSpecialFourfold) -- see surface -- get the special surface contained in the fourfold
• toExternalString(HodgeSpecialFourfold) -- convert to a readable string
• unirationalParametrization(HodgeSpecialFourfold) -- see unirationalParametrization -- unirational parametrization

For the programmer

The object HodgeSpecialFourfold is a type, with ancestor classes EmbeddedProjectiveVariety < MultiprojectiveVariety < MutableHashTable < HashTable < Thing.