Tensor complexes: Multilinear free resolutions constructed from higher tensors
2013 (English)In: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, Vol. 15, no 6, 2257-2295 p.Article in journal (Refereed) Published
The most fundamental complexes of free modules over a commutative ring are the Koszul complex, which is constructed from a vector (i.e., a 1-tensor), and the Eagon-Northcott and Buchsbaum-Rim complexes, which are constructed from a matrix (i.e., a 2-tensor). The subject of this paper is a multilinear analogue of these complexes, which we construct from an arbitrary higher tensor. Our construction provides detailed new examples of minimal free resolutions, as well as a unifying view on a wide variety of complexes including: the Eagon-Northcott, Buchsbaum-Rim and similar complexes, the Eisenbud-Schreyer pure resolutions, and the complexes used by Gelfand-Kapranov-Zelevinsky and Weyman to compute hyperdeterminants. In addition, we provide applications to the study of pure resolutions and Boij-Soderberg theory, including the construction of infinitely many new families of pure resolutions, and the first explicit description of the differentials of the Eisenbud-Schreyer pure resolutions.
Place, publisher, year, edition, pages
2013. Vol. 15, no 6, 2257-2295 p.
IdentifiersURN: urn:nbn:se:su:diva-97048DOI: 10.4171/JEMS/421ISI: 000326323400011OAI: oai:DiVA.org:su-97048DiVA: diva2:668932
NSF OISE 0964985,1003997; NDSEG2013-12-022013-12-022013-12-02Bibliographically approved