The Hilbert Scheme of 11 Points in \(\mathbb{A}^{3}\) Is Irreducible

  • Theodosios Douvropoulos
  • Joachim Jelisiejew
  • Bernt Ivar Utstøl Nødland
  • Zach TeitlerEmail author
Part of the Fields Institute Communications book series (FIC, volume 80)


We prove that the Hilbert scheme of 11 points on a smooth threefold is irreducible. In the course of the proof, we present several known and new techniques for producing curves on the Hilbert scheme.

MSC 2010 codes:

14C05 14D15 



This article was initiated during the Apprenticeship Weeks (22 August–2 September 2016), led by Bernd Sturmfels, as part of the Combinatorial Algebraic Geometry Semester at the Fields Institute. The authors wish to thank the Fields Institute, the organizers of the Thematic Program on Combinatorial Algebraic Geometry in Fall 2016, and the organizers of the Apprenticeship Weeks which took place during the program. We are very grateful to Mark Huibregtse, Anthony Iarrobino, Gary Kennedy, Greg Smith, Bernd Sturmfels, and several anonymous referees for numerous helpful comments. This work was supported by a grant from the Simons Foundation (#354574, Zach Teitler). JJ was supported by Polish National Science Center, project 2014/13/N/ST1/02640. BIUN was supported by NRC project 144013.


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© Springer Science+Business Media LLC 2017

Authors and Affiliations

  • Theodosios Douvropoulos
    • 1
  • Joachim Jelisiejew
    • 2
  • Bernt Ivar Utstøl Nødland
    • 3
  • Zach Teitler
    • 4
    Email author
  1. 1.Institut de Recherche en Informatique Fondamentale (IRIF)Université Paris DiderotParis Cedex 13France
  2. 2.Institute of MathematicsUniversity of WarsawWarszawaPoland
  3. 3.Department of MathematicsUniversity of OsloOsloNorway
  4. 4.Department of MathematicsBoise State UniversityBoiseUSA

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