Let
be a two-dimensional standard-graded normal domain over an algebraically closed field
. Let
be the corresponding smooth projective curve and let
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![{\displaystyle {}I={\left(f_{1},\ldots ,f_{n}\right)}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cbe0e095be425fc8946f1c9fbadd6cbf3ee152e6)
be an
-primary homogeneous ideal with generators of degrees
. Then we get on
the short exact sequence
-
Here
is a vector bundle, called the syzygy bundle, of rank
and of degree
-