Scheme of pairs of matrices with vanishing commutator


  • Bartomeu Llopis Vidal Universitat Politècnica de Catalunya


In this work we will study the scheme of n x n matrices with vanishing commutator,
which is conjectured to be reduced, Cohen{Macaulay and normal. We will prove
that it is regular in codimension 3 but not in codimension 4. We will also bring
similar results for other schemes related to our original one. In a second part of
the paper, we study the singularities of the scheme of pairs of commuting matrices
from the study of the corresponding jet schemes and other singularity invariants
such as the log-canonical threshold.

Keywords: commuting variety, jetschemes, log-canonical threshold.

Biografia de l'autor/a

Bartomeu Llopis Vidal, Universitat Politècnica de Catalunya


Com citar

Llopis Vidal, B. (2020). Scheme of pairs of matrices with vanishing commutator. Reports@SCM, 5(1), 23–32. Retrieved from