Canonical complexes associated to a matrix

Abstract

ABSTRACT. Let Φ be an f × g matrix with entries from a commutative Noetherian ring R, with g ≤ f. Recall the family of generalized Eagon-Northcott complexes {C i Φ } associated to Φ.

Hodge filtration on local cohomology, Du Bois complex and local cohomological dimension

“…Note that in our case, the ideal defines the singular locus of Z , and since Z is Cohen-Macaulay, the condition is equivalent to . The depth sensitivity of generalised Eagon-Northcott complexes is a consequence of the behavior in the case of generic matrices (see [5, Theorem 2.16]) and of general properties of perfect modules (see [30, Proposition 2.11.2]). In fact, the depth sensitivity of a more general class of complexes is proved in [30, Theorem 8.4].…”