A Linear Bound on the Projective Dimension of Height 3 Quadratic Ideals
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910223786049536 |
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| author | Greif, Zachary Mantero, Paolo McCullough, Jason |
| author_facet | Greif, Zachary Mantero, Paolo McCullough, Jason |
| contents | In 2016, Ananyan and Hochster gave the first proof of a positive answer to Stillman's Question, which asked for a bound on the projective dimension of a graded polynomial ideal purely in terms of the number and degrees of its generators. Explicit formulas for such a bound are limited and often not optimal. In this paper, we give a nearly optimal linear upper bound on the projective dimension of height $3$ ideals generated by any number of degree $2$ homogenous polynomials. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_15992 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Linear Bound on the Projective Dimension of Height 3 Quadratic Ideals Greif, Zachary Mantero, Paolo McCullough, Jason Commutative Algebra Primary: 13D02, 13C10, Secondary: 14M07 In 2016, Ananyan and Hochster gave the first proof of a positive answer to Stillman's Question, which asked for a bound on the projective dimension of a graded polynomial ideal purely in terms of the number and degrees of its generators. Explicit formulas for such a bound are limited and often not optimal. In this paper, we give a nearly optimal linear upper bound on the projective dimension of height $3$ ideals generated by any number of degree $2$ homogenous polynomials. |
| title | A Linear Bound on the Projective Dimension of Height 3 Quadratic Ideals |
| topic | Commutative Algebra Primary: 13D02, 13C10, Secondary: 14M07 |
| url | https://arxiv.org/abs/2605.15992 |