Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 039-01. Nagata's conjecture for plane curves
Manuscript map · lines 3355–3364
OpenAI@2026-10-07#rem:oai-p-039-01
Authors: OpenAI. Family 039.
Title: Nagata's conjecture for plane curves.
Abstract: We prove that a nonzero effective plane curve of degree d at r ≥ 10 very general complex points has total multiplicity strictly less than $d{}sqrt r$. The inequality holds simultaneously for all curves, including reducible and nonreduced curves, and establishes Nagata's conjecture in its strict, nonhomogeneous form.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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