project -- project a K3 surface

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