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Tensor complexes: multilinear free resolutions constructed from higher tensors

Christine Berkesch Zamaere, Daniel Erman, Manoj Kummini, Steven V. Sam (2013)

Journal of the European Mathematical Society

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...

The determinant line bundle over moduli spaces of instantons on abelian surfaces.

Antony Maciocia (1994)

Mathematische Zeitschrift

The dimension of certain catalecticant varieties.

Aldo Conca, Giuseppe Valla (2004)

Collectanea Mathematica

The discriminants of curves of genus 2

Takeshi Saito (1989)

Compositio Mathematica

The existence of equivariant pure free resolutions

David Eisenbud, Gunnar Fløystad, Jerzy Weyman (2011)

Annales de l’institut Fourier

Let $A = K [x_{1}, \dots, x_{m}]$ be a polynomial ring in $m$ variables and let $d = (d_{0} < \dots < d_{m})$ be a strictly increasing sequence of $m + 1$ integers. Boij and Söderberg conjectured the existence of graded $A$ -modules $M$ of finite length having pure free resolution of type $d$ in the sense that for $i = 0, \dots, m$ the $i$ -th syzygy module of $M$ has generators only in degree $d_{i}$ .This paper provides a construction, in characteristic zero, of modules with this property that are also $G L (m)$ -equivariant. Moreover, the construction works over rings of the form $A \otimes_{K} B$ where $A$ is a polynomial...