The punctual Hilbert scheme of 4 points in affine 3-space via computer algebra and representation theory

  • Balazs Szendroi (University of Oxford)
Live Stream


The n-th punctual Hilbert scheme $Hilb^n_0(A^d)$ of points of affine d-space parametrises ideals of finite co-length n of the ring of functions on d-dimensional affine space, whose radical is the maximal ideal at the origin (equivalently, subschemes of length n with support at the origin). A classical theorem of Briancon claims the irreducibility of this space for d=2 and arbitrary n. The case of a small number of points being straightforward, the first nontrivial case is the case of 4 points in 3-space. We show, answering a question of Sturmfels, that over the complex numbers $Hilb^4_0(A^3)$ is irreducible. We use a combination of arguments from computer algebra and representation theory.


17.03.20 21.02.22

Nonlinear Algebra Seminar Online (NASO)

MPI for Mathematics in the Sciences Live Stream

Katharina Matschke

MPI for Mathematics in the Sciences Contact via Mail