-- Example 10a: the genus 10 tangent developable
load "MukaiModels.m2";
S = QQ[H_2,X_1,X_2,X_4,X_5,X_6,Y_1,Y_2,Y_4,Y_5,Y_6];
H_1 = 4/9*H_2;
X_3 = 4/27*Y_6;
Y_3 = 5/4*X_6;
LTD10={H_1-4/9*H_2, X_3-4/27*Y_6, Y_3-5/4*X_6};
all(LTD10, i -> i==0)
PcapG2AdjVar = {Y_4^2+Y_3*Y_5-Y_1*Y_6,
Y_3*Y_4+Y_2*Y_5+2*H_1*Y_6-H_2*Y_6,
Y_1*Y_4-H_1*Y_5+H_2*Y_5+X_2*Y_6,
H_1*Y_4+X_1*Y_5+X_3*Y_6,
Y_3^2-Y_2*Y_4+X_1*Y_6,
Y_1*Y_3-H_2*Y_4-X_1*Y_5-2*X_3*Y_6,
H_1*Y_3-X_1*Y_4-X_4*Y_6,
Y_1*Y_2-H_2*Y_3+X_1*Y_4+2*X_4*Y_6,
H_1*Y_2-X_1*Y_3-X_5*Y_6,
Y_1^2+X_2*Y_4-X_3*Y_5,
X_1*Y_1+X_3*Y_3+X_4*Y_4,
H_2*Y_1+X_2*Y_3+2*X_3*Y_4-X_4*Y_5,
H_1*Y_1+X_3*Y_4-X_4*Y_5,
X_4^2+X_3*X_5-X_1*X_6,
X_3*X_4+X_2*X_5+2*H_1*X_6-H_2*X_6,
X_1*X_4-H_1*X_5+H_2*X_5+X_6*Y_2,
H_1*X_4+X_5*Y_1+X_6*Y_3,
X_3^2-X_2*X_4+X_6*Y_1,
X_1*X_3-H_2*X_4-X_5*Y_1-2*X_6*Y_3,
H_1*X_3-X_4*Y_1-X_6*Y_4,
X_1*X_2-H_2*X_3+X_4*Y_1+2*X_6*Y_4,
H_1*X_2-X_3*Y_1-X_6*Y_5,
X_1^2+X_4*Y_2-X_5*Y_3,
H_2*X_1+X_3*Y_2+2*X_4*Y_3-X_5*Y_4,
H_1*X_1+X_4*Y_3-X_5*Y_4,
H_2^2+X_2*Y_2+3*X_3*Y_3+3*X_4*Y_4+X_5*Y_5+4*X_6*Y_6,
H_1*H_2+X_3*Y_3+2*X_4*Y_4+X_5*Y_5+2*X_6*Y_6,
H_1^2+X_4*Y_4+X_5*Y_5+X_6*Y_6};
R=QQ[y_0..y_10];
TD10 = schreyerTangentDevelopableQuadrics(gens R);
F = map(R,S,{-(9/5)*y_5, (1/5)*y_8, -(1/3)*y_1, (4/15)*y_7, -(2/75)*y_10, (2/5)*y_6, -(1/2)*y_2, -(1/5)*y_9, y_3, (1/4)*y_0, -(9/4)*y_4});
F(ideal PcapG2AdjVar)==ideal(TD10)