For any homogeneous ideal I in a polynomial algebra over an algebraically closed field k,
a syzygy of I is a relation between the generators of I. Higher syzygies, built inductively
(relations between relations etc), seem to hide intrinsic properties of the projective variety
X defined by I. We shall discuss some recent developments in the syzygy theory, with
emphasis on the curve case.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/node/158