Determinantal representation of a class of surfaces
In 3-dimensional projective space over a field \(K\) with \(\text{char} (K)\neq 2\) an algebraic surface \(\Phi\) of degree 4 is said to have a determinantal representation, if its equation can be written as the determinant of a (4,4)-matrix with elements being homogeneous linear polynomials of the coordinates. The author studies those surfaces of degree 4 which contain two straight lines \(r\) and \(s\) (multiplicity \(\mu_r, \mu_s\) resp.) with \(\mu_r+ \mu_s=4\). She is able to prove that each of these surfaces with multiplicities \((\mu_r, \mu_s)= (1,3)\) or (3,1) admits a determinantal representation. In the case \((\mu_r, \mu_s)= (2,2)\) she characterizes the surfaces of degree 4 with determinantal representations.
scientific article; zbMATH DE number 1019775
scientific article