surface -- get the special surface contained in the fourfold

Usage:

surface X
Inputs:
- X, a Hodge-special fourfold
Outputs:
- an embedded projective variety, the special surface contained in the fourfold X

Description

i1 : X = specialFourfold "quintic del Pezzo surface";

o1 : ProjectiveVariety, GM fourfold containing a surface of degree 5 and sectional genus 1

i2 : V = ambientFivefold X;

o2 : ProjectiveVariety, 5-dimensional subvariety of PP^8

i3 : S = surface X;

o3 : ProjectiveVariety, surface in PP^8 (subvariety of codimension 3 in V)

i4 : assert isSubset(S,X)

surface(HodgeSpecialFourfold)
surface(List) -- get a rational surface
surface(VisibleList,Option) -- see surface(List) -- get a rational surface
surface(VisibleList,Option,Option) -- see surface(List) -- get a rational surface
surface(VisibleList,Ring) -- see surface(List) -- get a rational surface
surface(VisibleList,Ring,Option) -- see surface(List) -- get a rational surface
surface(VisibleList,Ring,Option,Option) -- see surface(List) -- get a rational surface
surface(MultiprojectiveVariety,MultiprojectiveVariety) -- make a Hodge-special surface

The source of this document is in SpecialFanoFourfolds.m2:3435:0.