Monomial curves and locally linear resolution

Takayuki Hibi; Peter Schenzel

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arXiv · 2510.04412

Monomial curves and locally linear resolution

Takayuki Hibi·Peter Schenzel

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Abstract

For four elements of a Noetherian ring we construct complexes of free modules of length three (resp. five) by an explicit description of the homomorphisms of the free modules. We provide exactness criteria for them. As an application we use these results in order to describe explicit the minimal free resolution of the Hartshorne--Rao module of a monomial curve lying on a smooth quadric. Also it provides an example of linearly generated module with syzygies of arbitrary high degree.

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Takayuki Hibi, Peter Schenzel. 2025-10-06. Monomial curves and locally linear resolution. https://arxiv.org/abs/2510.04412

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