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Linear strands of multigraded free resolutions

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Abstract

We develop a notion of linear strands for multigraded free resolutions, and we prove a multigraded generalization of Green’s Linear Syzygy Theorem.

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Notes

  1. This characterization relies on the fact that M is generated entirely in degree 0; see Remark 5.4.

  2. See [3, §3.1] for our definition of a projective toric stack, as well as a discussion of the relationship between a toric stack and its corresponding toric variety. When X is smooth, there is no distinction; but as in other algebraic investigations of toric geometry, sheaves are generally better behaved on the toric stack than on the corresponding toric variety.

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Acknowledgements

We thank David Eisenbud, Hal Schenck, and Frank-Olaf Schreyer for valuable conversations. We are also grateful to the referee for helpful comments that improved this paper.

Funding

The first author was supported by NSF-RTG grant 1502553. The second author was supported by NSF grants DMS-1601619 and DMS-1902123.

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Authors and Affiliations

  1. Department of Mathematics, Auburn University, 221 Roosevelt Con., Auburn, AL, 36849, USA

    Michael K. Brown

  2. Department of Mathematics, University of Hawaii at Manoa, 2565, McCarthy Mall, Honolulu, HI, 96822, USA

    Daniel Erman

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  1. Michael K. Brown
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Correspondence to Daniel Erman.

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Brown, M.K., Erman, D. Linear strands of multigraded free resolutions. Math. Ann. (2024). https://doi.org/10.1007/s00208-024-02803-1

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