surface                                                                  field   d  pi  d-1+pi  dim W  lines  F in I(l)^2  W=0 on lines  ok
cone over the nodal cubic  z^2 w = y^2 (y + w)                           Q       3   0       2      2      1  True         True          True
cone over the nodal cubic  z^2 w = y^2 (y + w)                           F_5     3   0       2      2      1  True         True          True
cone over the cuspidal cubic  z^2 w = y^3                                Q       3   0       2      2      1  True         True          True
cone over the cuspidal cubic  z^2 w = y^3                                F_2     3   0       2      2      1  True         True          True
cone over the cuspidal cubic  z^2 w = y^3                                F_3     3   0       2      2      1  True         True          True
cone over a quartic with three nodes                                     Q       4   0       3      3      3  True         True          True
cone over the quartic  z^4 = y^3 w  (unibranch triple point)             Q       4   0       3      3      1  True         True          True
cone over the quartic  z^4 = y^3 w  (unibranch triple point)             F_3     4   0       3      3      1  True         True          True
cone over the quintic  z^5 = y^2 w^3                                     Q       5   0       4      4      2  True         True          True
cone over the sextic  z^6 = y^5 w  (unibranch five-fold point)           Q       6   0       5      5      1  True         True          True
ruled cubic  x^2 z = y^2 w  (double line)                                Q       3   0       2      2      1  True         True          True
ruled cubic  x^2 z = y^2 w  (double line)                                F_2     3   0       2      2      1  True         True          True
ruled quartic  x^3 z = y^3 w  (triple line)                              Q       4   0       3      3      1  True         True          True
ruled quartic  x^3 z = y^3 w  (triple line)                              F_3     4   0       3      3      1  True         True          True
ruled quartic  z A = w B, general cubics A, B  (triple line)             Q       4   0       3      3      1  True         True          True
ruled quintic  z A = w B, general quartics A, B  (four-fold line)        Q       5   0       4      4      1  True         True          True
ruled sextic  z A = w B, general quintics A, B  (five-fold line)         Q       6   0       5      5      1  True         True          True
x^2 w = z^2 y in characteristic 2  (inseparable 2-fold line)             F_2     3   0       2      2      1  True         True          True
x^3 w = z^3 y in characteristic 3  (inseparable 3-fold line)             F_3     4   0       3      3      1  True         True          True
x^5 w = z^5 y in characteristic 5  (inseparable 5-fold line)             F_5     6   0       5      5      1  True         True          True
Steiner's Roman surface  x^2y^2 + y^2z^2 + z^2x^2 = xyzw                 Q       4   0       3      3      3  True         True          True
Steiner's Roman surface  x^2y^2 + y^2z^2 + z^2x^2 = xyzw                 F_3     4   0       3      3      3  True         True          True
x^2 y^2 = z^3 w  (two double lines meeting in a point)                   Q       4   1       4      5      2  True         True          True
x^2 y^3 = z^4 w  (a double and a triple line meeting in a point)         Q       5   1       5      6      2  True         True          True
x^2 y^2 = z^3 w  (two double lines meeting in a point)                   F_5     4   1       4      5      2  True         True          True
x^2 y^3 = z^4 w  (a double and a triple line meeting in a point)         F_5     5   1       5      6      2  True         True          True
quartic with two skew double lines (bidegree (2,2)) I                    Q       4   1       4      4      2  True         True          True
quartic with two skew double lines (bidegree (2,2)) II                   Q       4   1       4      4      2  True         True          True
quartic with two skew double lines (bidegree (2,2)) III                  F_7     4   1       4      4      2  True         True          True
quartic with two skew double lines (bidegree (2,2)) IV                   F_5     4   1       4      4      2  True         True          True
quintic with a double and a triple line (bidegree (2,3)) I               Q       5   2       6      6      2  True         True          True
quintic with a double and a triple line (bidegree (2,3)) II              F_11    5   2       6      6      2  True         True          True
sextic with a double and a four-fold line (bidegree (2,4))               Q       6   3       8      8      2  True         True          True

surfaces computed: 33; all checks hold: True; degrees: [3, 4, 5, 6]; dim W = d-1+pi in 29 cases, > d-1+pi in 4 cases
