Hilbert–Burch theorem

In mathematics, the Hilbert–Burch theorem describes the structure of some free resolutions of a quotient of a local or graded ring in the case that the quotient has projective dimension 2.

Hilbert (1890) proved a version of this theorem for polynomial rings, and Burch (1968, p. 944) proved a more general version.

Several other authors later rediscovered and published variations of this theorem.

Eisenbud (1995, theorem 20.15) gives a statement and proof.

of I, i.e., the ideal generated by the determinants of the minors of size m of the matrix of f.