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arXiv · 2606.14596

Higher syzygy bundles and the Eisenbud-Huneke-Ulrich conjecture

Fuxiang Yang
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Abstract

We study ideals in a polynomial ring with partially linear (virtual) resolutions. We establish an effective bound beyond which their powers coincide with a power of the maximal ideal, proving a slightly weaker version of the Eisenbud-Huneke-Ulrich conjecture for a more general class of ideals. We also obtain an upper bound on their Castelnuovo-Mumford regularity, extending Macaulay's bound and a theorem of Eisenbud-Huneke-Ulrich. We introduce higher syzygy bundles, which generalize the classical Green-Lazarsfeld syzygy bundle. The key ingredient is the relationship between the syzygies of partially linear ideals and the sheaf cohomology of higher syzygy bundles.

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Fuxiang Yang. 2026-06-12. Higher syzygy bundles and the Eisenbud-Huneke-Ulrich conjecture. https://arxiv.org/abs/2606.14596

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