EXTERIOR DEPTH AND EXTERIOR GENERIC ANNIHILATOR NUMBERS

Abstract

We study the exterior depth of an E-module and its exterior generic annihilator numbers. For the exterior depth of a squarefree E-module, we show how it relates to the symmetric depth of the corresponding S-module and classify those simplicial complexes having a particular exterior depth in terms of their exterior algebraic shifting. We define exterior annihilator numbers analogously to the annihilator numbers over the polynomial ring introduced by Trung [19] and Conca et al. [9]. In addition to a combinatorial interpretation of the annihilator numbers, we show how they are related to the symmetric Betti numbers and the Cartan-Betti numbers, respectively. We finally conclude with an example which shows that neither the symmetric nor the exterior generic annihilator numbers are minimal among the annihilator numbers with respect to a sequence.