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Hilbert functions of chopped ideals of general plane points

Primarily AI-generated textHuman understanding: all partsmath.AC — Commutative Algebra

Contributed by Vlado Vojdanovski

Version 2 / Oct 13, 2026 / CC BY 4.0

Abstract

Let Z be a finite set of general points in the projective plane over a field of character- istic zero. We determine the Hilbert function of the ideal generated by the degree-d equations of Z, for every d. This proves the plane case of the Expected Syzygy Conjecture. The proof realizes the quotient of the point ideal by its degree-d equations as the cokernel of a linear block in a Hilbert–Burch matrix, and applies natural cohomology for general plane Steiner bundles.

Formalizations

References

  1. I. Coskun, J. Huizenga, and G. Smith, Stability and cohomology of kernel bundles on Pn\mathbb P^n , Michigan Math. J. 75 (2025), no. 1, 173--198. doi:10.1307/mmj/20226238 (https://doi.org/10.1307/mmj/20226238).DOI
  2. D. Eisenbud, Commutative Algebra: with a View Toward Algebraic Geometry , Graduate Texts in Mathematics, vol. 150, Springer-Verlag, New York, 1995. doi:10.1007/978-1-4612-5350-1 (https://doi.org/10.1007/978-1-4612-5350-1).DOI
  3. F. Gesmundo, L. Kayser, and S. Telen, Hilbert functions of chopped ideals , J. Algebra 666 (2025), 415--445. doi:10.1016/j.jalgebra.2024.11.017 (https://doi.org/10.1016/j.jalgebra.2024.11.017).DOI

Version history

  1. v1Submitted by Vlado VojdanovskiInitial depositSupersededOct 13, 2026
  2. v2Submitted by Vlado VojdanovskiSubmitted as a new versionCurrentOct 13, 2026