Tensor complexes: multilinear free resolutions constructed from higher tensors

Berkesch Zamaere, Christine, et al. "Tensor complexes: multilinear free resolutions constructed from higher tensors." Journal of the European Mathematical Society 015.6 (2013): 2257-2295. <http://eudml.org/doc/277785>.

@article{BerkeschZamaere2013,
abstract = {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–Söderberg 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.},
author = {Berkesch Zamaere, Christine, Erman, Daniel, Kummini, Manoj, Sam, Steven V.},
journal = {Journal of the European Mathematical Society},
keywords = {free resolutions; tensors; hyperdeterminant; free resolutions; tensors; hyperdeterminant},
language = {eng},
number = {6},
pages = {2257-2295},
publisher = {European Mathematical Society Publishing House},
title = {Tensor complexes: multilinear free resolutions constructed from higher tensors},
url = {http://eudml.org/doc/277785},
volume = {015},
year = {2013},
}

TY - JOUR
AU - Berkesch Zamaere, Christine
AU - Erman, Daniel
AU - Kummini, Manoj
AU - Sam, Steven V.
TI - Tensor complexes: multilinear free resolutions constructed from higher tensors
JO - Journal of the European Mathematical Society
PY - 2013
PB - European Mathematical Society Publishing House
VL - 015
IS - 6
SP - 2257
EP - 2295
AB - 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–Söderberg 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.
LA - eng
KW - free resolutions; tensors; hyperdeterminant; free resolutions; tensors; hyperdeterminant
UR - http://eudml.org/doc/277785
ER -