Abstract: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.
| Comments: | 27 pages, 2 figures |
| Subjects: | Algebraic Geometry (math.AG) |
| MSC classes: | 14H51, 14C20, 14H10, 14N07 |
| Cite as: | arXiv:2605.24612 [math.AG] |
| (or arXiv:2605.24612v1 [math.AG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24612 arXiv-issued DOI via DataCite (pending registration) |
From: Vlad Robu [view email]
[v1]
Sat, 23 May 2026 14:50:42 UTC (97 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。