Nagata's conjecture for plane curves
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.
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On OpenAI's proof of the Nagata conjecturearXiv.orgJenia TevelevOct 21, 2026in the index
These notes are an expanded account of my talk at UMass Amherst on OpenAI's remarkably simple proof of the Nagata conjecture. I hope they will be useful, especially to non-experts. The standard reduction to the normal cone and the collision of fat points into one monomial scheme reduce the problem…