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arXiv · 2605.09143

Quadratic linear strands of prime ideals

Giulio Caviglia·Alessandro De Stefani
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Abstract

We prove sharp estimates on the quadratic strand of the resolution of any homogeneous prime ideal in a standard graded polynomial ring over an arbitrary field. Our bounds only depend on the height of the prime ideal, and they are optimal since for every $h \geq 1$ we show that there exists a prime ideal of height $h$ achieving them. In particular, we show that a prime ideal of height $h$ can contain at most $h^2$ quadratic minimal generators, and that there exists a prime ideal minimally generated by $h^2$ quadrics.

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Giulio Caviglia, Alessandro De Stefani. 2026-05-09. Quadratic linear strands of prime ideals. https://arxiv.org/abs/2605.09143

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