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Nagata’s plane-curve conjecture

Square values of the point count were covered by Nagata’s original cases.

Progress records 1

Understand the problem ↓

1 record · How we rate progress

Understanding the problem

Read the background

Square values of the point count were covered by Nagata’s original cases. The unresolved target includes all point counts at least ten and unequal assigned multiplicities.

Very general points are required; arbitrary configurations are not covered. The strict inequality does not start at nine points and does not describe every special interpolation problem.

Why it matters

If correct, extends the square-root interpolation bound to all stated point counts and nonhomogeneous multiplicities.

What counts as progress

A sourced resolution or substantial advance on the precise target, with hypotheses, prior context, and verification evidence stated separately.

What to watch for

  • Assess the precise statement and assumptions before comparing results.
  • Very general points are required; arbitrary configurations are not covered. The strict inequality does not start at nine points and does not describe every special interpolation problem.
  • Track independent assessments, dependencies, corrections, and withdrawals separately from importance.

Background review: 2026-10-11. Selected sources:

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Publication dates and editorial changes.