SpecialFanoFourfolds -- A (work-in-progress) package for working with special cubic fourfolds and special Gushel-Mukai fourfolds

Author

Giovanni Staglianò <giovannistagliano@gmail.com>

Version

This documentation describes version 0.9.2 of SpecialFanoFourfolds.

Source code

The source code from which this documentation is derived is in the file SpecialFanoFourfolds.m2.

Exports

Types
- SpecialCubicFourfold -- the class of all special cubic fourfolds
- SpecialGushelMukaiFourfold -- the class of all special Gushel-Mukai fourfolds
Functions and commands
- coneOfLines -- cone of lines on a subvariety passing through a point
- cycleClass -- determine the expression of the class of a cycle as a linear combination of Schubert classes
- detectCongruence -- detect and return a congruence of (3e-1)-secant curves of degree e
- grassmannianHull -- grassmannian hull of a Gushel-Mukai fourfold
- ideals -- corresponding ideals
- isAdmissible -- whether an integer is admissible
- normalSheaf -- normal sheaf
- parameterCount -- count of parameters
- schubertCycle -- take a random Schubert cycle
- specialCubicFourfold -- make a special cubic fourfold
- specialGushelMukaiFourfold -- make a special Gushel-Mukai fourfold
- tables -- make examples of reducible subschemes of P^5
- toGrass -- Gushel morphism from a GM fourfold to Grass(1,4)
- unirationalParametrization -- unirational parametrization
Methods
- < SpecialGushelMukaiFourfold -- try to deform to a fourfold of Gushel type
- detectCongruence(SpecialCubicFourfold), see detectCongruence -- detect and return a congruence of (3e-1)-secant curves of degree e
- detectCongruence(SpecialCubicFourfold,ZZ), see detectCongruence -- detect and return a congruence of (3e-1)-secant curves of degree e
- detectCongruence(SpecialGushelMukaiFourfold), see detectCongruence -- detect and return a congruence of (3e-1)-secant curves of degree e
- detectCongruence(SpecialGushelMukaiFourfold,ZZ), see detectCongruence -- detect and return a congruence of (3e-1)-secant curves of degree e
- discriminant(SpecialCubicFourfold) -- discriminant of a special cubic fourfold
- discriminant(SpecialGushelMukaiFourfold) -- discriminant of a special Gushel-Mukai fourfold
- grassmannianHull(SpecialGushelMukaiFourfold), see grassmannianHull -- grassmannian hull of a Gushel-Mukai fourfold
- ideal(SpecialCubicFourfold) -- ideal of the fourfold
- ideal(SpecialGushelMukaiFourfold), see ideal(SpecialCubicFourfold) -- ideal of the fourfold
- ideals(SpecialCubicFourfold), see ideals -- corresponding ideals
- ideals(SpecialGushelMukaiFourfold), see ideals -- corresponding ideals
- isAdmissible(SpecialCubicFourfold), see isAdmissible -- whether an integer is admissible
- map(SpecialCubicFourfold) -- associated cubic map
- map(SpecialGushelMukaiFourfold) -- associated quadratic map
- parameterCount(SpecialCubicFourfold), see parameterCount -- count of parameters
- parameterCount(SpecialGushelMukaiFourfold) -- count of parameters in the moduli space of GM fourfolds
- parametrize(SpecialCubicFourfold) -- rational parametrization
- parametrize(SpecialGushelMukaiFourfold), see parametrize(SpecialCubicFourfold) -- rational parametrization
- ring(SpecialCubicFourfold) -- ambient polynomial ring of the fourfold
- ring(SpecialGushelMukaiFourfold), see ring(SpecialCubicFourfold) -- ambient polynomial ring of the fourfold
- toGrass(SpecialGushelMukaiFourfold), see toGrass -- Gushel morphism from a GM fourfold to Grass(1,4)
- unirationalParametrization(SpecialCubicFourfold), see unirationalParametrization -- unirational parametrization
- unirationalParametrization(SpecialCubicFourfold,Ideal), see unirationalParametrization -- unirational parametrization
- unirationalParametrization(SpecialGushelMukaiFourfold), see unirationalParametrization -- unirational parametrization
Symbols