The Stratified and the Strong Maximal Rank Conjecture in $\mathbb{P}^3$ and $\mathbb{P}^4$
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866916042258776064 |
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| author | Robu, Vlad |
| author_facet | Robu, Vlad |
| contents | We prove that the Strong Maximal Rank Conjecture holds for quadrics in $\mathbb{P}^3$ and we prove the existence of a component of the expected dimension in $\mathbb{P}^4$, as well as in a wide range of parameters $(g,d)$ in $\mathbb{P}^r$ with $r\ge 5$. We propose the Stratified Strong Maximal Rank Conjecture which also takes into account the rank $k$ of quadrics and prove it works in most of the cases when $k=3$ and $k=4$. We also prove a partial result that concerns the unrepresentability of the canonical bundle of a general curve as a sum of $3$ pencils. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24612 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Stratified and the Strong Maximal Rank Conjecture in $\mathbb{P}^3$ and $\mathbb{P}^4$ Robu, Vlad Algebraic Geometry 14H51, 14C20, 14H10, 14N07 We prove that the Strong Maximal Rank Conjecture holds for quadrics in $\mathbb{P}^3$ and we prove the existence of a component of the expected dimension in $\mathbb{P}^4$, as well as in a wide range of parameters $(g,d)$ in $\mathbb{P}^r$ with $r\ge 5$. We propose the Stratified Strong Maximal Rank Conjecture which also takes into account the rank $k$ of quadrics and prove it works in most of the cases when $k=3$ and $k=4$. We also prove a partial result that concerns the unrepresentability of the canonical bundle of a general curve as a sum of $3$ pencils. |
| title | The Stratified and the Strong Maximal Rank Conjecture in $\mathbb{P}^3$ and $\mathbb{P}^4$ |
| topic | Algebraic Geometry 14H51, 14C20, 14H10, 14N07 |
| url | https://arxiv.org/abs/2605.24612 |