HodgeSpecialFourfold -- the class of all Hodge-special fourfolds

Description

An object of the class HodgeSpecialFourfold is basically represented by a couple (S,X), where $X$ is a fourfold and $S$ is a surface contained in $X$. Such objects are created by the function specialFourfold.

Types of `Hodge-special fourfold` :

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
"mirrorFourfold(HodgeSpecialFourfold)" -- see mirrorFourfold -- associated fourfold to a rational cubic or GM fourfold
"parameterCount(HodgeSpecialFourfold)" -- see parameterCount -- count of parameters
"parameterCount(HodgeSpecialFourfold,EmbeddedProjectiveVariety)" -- 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.