Mathematics – Commutative Algebra
Scientific paper
2011-01-24
Mathematics
Commutative Algebra
37 pages; v2: The material on hyperdeterminantal varieties is significantly clarified and strengthened; v3: Conjecture 1.10
Scientific paper
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 the 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-Soederberg 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.
Berkesch Christine
Erman Daniel
Kummini Manoj
Sam Steven V.
No associations
LandOfFree
Tensor complexes: Multilinear free resolutions constructed from higher tensors does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Tensor complexes: Multilinear free resolutions constructed from higher tensors, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Tensor complexes: Multilinear free resolutions constructed from higher tensors will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-638139