# Characterizing Multigraded Regularity on Products of Projective Spaces

@inproceedings{Bruce2021CharacterizingMR, title={Characterizing Multigraded Regularity on Products of Projective Spaces}, author={Juliette Bruce and Lauren Heller and Mahrud Sayrafi}, year={2021} }

We explore the relationship between multigraded Castelnuovo–Mumford regularity, truncations, Betti numbers, and virtual resolutions. We prove that on a product of projective spaces X , the multigraded regularity region of a module M is determined by the minimal graded free resolutions of the truncations M≥d for d ∈ PicX . Further, by relating the minimal graded free resolutions of M and M≥d we provide a new bound on multigraded regularity of M in terms of its Betti numbers. Using this…

## 4 Citations

A C ] 2 6 N ov 2 02 1 VIRTUAL CRITERION FOR GENERALIZED EAGON-NORTHCOTT COMPLEXES CAITLYN BOOMS

- 2021

Given any map of finitely generated free modules, Buchsbaum and Eisenbud define a family of generalized Eagon-Northcott complexes associated to it [BE75]. We give sufficient criterion for these…

Linear Truncations Package for Macaulay2

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- 2021

We introduce the Macaulay2 package LinearTruncations for finding and studying the truncations of a multigraded module over a standard multigraded ring that have linear resolutions.

Tate resolutions on toric varieties

- Mathematics
- 2021

We develop an analogue of Eisenbud-Fløystad-Schreyer’s Tate resolutions for toric varieties. Our construction, which is given by a noncommutative analogue of a FourierMukai transform, works quite…

Virtual criterion for generalized Eagon-Northcott complexes

- Mathematics
- 2021

Given any map of finitely generated free modules, Buchsbaum and Eisenbud define a family of generalized Eagon-Northcott complexes associated to it [BE75]. We give sufficient criterion for these…

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