Maximal Rank Conjecture for the restriction maps

At least 8 years old · documented by 2017

Let the restriction maps be those in Theorem, and let $d\geqslant 1$ . The paper reports that no counterexamples were found in the tested range $d<d_0(m)$ . Maximal Rank Conjecture. The restriction maps in Theorem have maximal rank for all $d\geqslant 1$ . This is proposed because the computations found no failures below the stated threshold; the general assertion remains open in the source.

References

Primary source

Thomas Bauer, Sandra Di Rocco, David Schmitz, Tomasz Szemberg and Justyna Szpond, “On the postulation of lines and a fat line”, arXiv:1706.02350 (2017).

Posted 1 month ago

Progress summary

Refreshed 1 month ago

Open

No verified progress on this conjecture was found; only finite computations support it, and the general assertion remains open.

No relevant proof, counterexample, verification, or claimed settlement of this exact conjecture was found. A similarly named conjecture for restriction maps of general Brill–Noether curves was proved by Eric Larson in 2017, with a 2018 exposition, but the retrieved sources do not identify those maps with the maps here or address the threshold $d_0(m)$ .

Current status (as of August 2026): the conjecture remains open; only the reported computations for $d<d_0(m)$ , with no detected counterexamples, are settled.

Sources

arxiv.org

No solutions have been posted yet.