project -- project a K3 surface

Synopsis

Usage:

project({i,j,k,...},S,a,b)

project({i,j,k,...},S(a,b))
Inputs:
- a visible list, a list $\{i,j,k,\ldots\}$ of nonnegative integers
- S, a K3 surface, a lattice-polarized K3 surface with rank 2 lattice spanned by $H,C$
- a, an integer
- b, an integer
Outputs:
- an embedded projective variety, the projection of $S$ embedded by the complete linear system $|a H + b C|$ from $i$ random points of multiplicity 1, $j$ random points of multiplicity 2, $k$ random points of multiplicity 3, and so on until the last integer in the given list.

Description

i1 : S = K3(8,2,-2)

o1 = K3 surface with rank 2 lattice defined by the intersection matrix: | 14 2  |
                                                                        | 2  -2 |
     -- (1,0): K3 surface of genus 8 and degree 14 containing rational curve of degree 2 (cubic fourfold) 
     -- (2,0): K3 surface of genus 29 and degree 56 containing rational curve of degree 4 
     -- (2,1): K3 surface of genus 32 and degree 62 containing rational curve of degree 2 (cubic fourfold) 


o1 : Lattice-polarized K3 surface

i2 : project({5,3,1},S,2,1); -- (5th + 3rd + simple)-projection of S(2,1)
-- *** simulation ***
-- surface of degree 62 and sectional genus 32 in PP^32 (quadrics: 435, cubics: 6264)
-- surface of degree 37 and sectional genus 22 in PP^17 (quadrics: 100, cubics: 979)
-- surface of degree 28 and sectional genus 19 in PP^11 (quadrics: 28, cubics: 248)
-- surface of degree 27 and sectional genus 19 in PP^10 (quadrics: 19, cubics: 176)

-- (degree and genus are as expected)

o2 : ProjectiveVariety, surface in PP^10

Ways to use project :

project(VisibleList,EmbeddedK3surface)
project(VisibleList,LatticePolarizedK3surface,ZZ,ZZ)

For the programmer

The object project is a method function.

project -- project a K3 surface

Synopsis

Description

See also

Ways to use project :

For the programmer