| It
is classically known that the defining equation of any algebraic plane
curve can be represented as the determinant of a matrix whose entries
are linear forms. Such representations are well studied for the case of
smooth curves. For example, the left and right kernels of the matrix
define specific line bundles. And the determinantal representation is
determined uniquely by such bundles. The theory can be extended to
singular and even non-reduced curves (then line bundles are replaced by
vector bundles or torsion free sheaves). I will give a brief
introduction and report on the recent result: the classification of the
'maximal' determinantal representations over curves with arbitrary
singularities. (joint with V.Vinnikov, BGU) |