Null-quadrics of codimension 4 in \(\mathbb{C}^7\)
The author classifies the null-quadrics of type (4,3) and finds their automorphism groups. Any null-quadric of codimension 4 in \(\mathbb C^7\) is equivalent either to the quadric \(Q_1\) or to the quadric \(Q_2,\) where \[ \langle z,z\rangle^1_1=2 \text{Re} z^1z^3, \langle z,z\rangle^2_1=2 \text{Re} z^2z^3, \langle z,z\rangle^3_1=2 \text{Im} z^1z^3, \langle z,z\rangle^4_1=2 \text{Im} z^2z^3, \] \[ \langle z,z\rangle^1_2=2 \text{Re} z^1z^3, \langle z,z\rangle^2_2=2 \text{Re} z^2z^3, \langle z,z\rangle^3_2=| z^3|^2, \langle z,z\rangle^4_2=2 \text{Im} z^2z^3. \] The quadrics \(Q_1\) and \(\mathbb Q_2\) are not equivalent.
scientific article; zbMATH DE number 1257153