HodgeSpecialFourfold -- the class of all Hodge-special fourfolds

Description

An object of the class HodgeSpecialFourfold is basically represented by a pair (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:

CubicFourfold -- the class of all special cubic fourfolds
GushelMukaiFourfold -- the class of all special Gushel-Mukai fourfolds
IntersectionOfThreeQuadricsInP7 -- the class of all special intersection of three quadrics in P^7

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(CubicFourfold) -- 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.

The source of this document is in SpecialFanoFourfolds/docs.m2:495:0.