Scheme of pairs of matrices with vanishing commutator

• Bartomeu Llopis Vidal ^[1]
  1. [1] Universitat Politècnica de Catalunya

     Universitat Politècnica de Catalunya

     Barcelona, España

     
• Localización: Reports@SCM: an electronic journal of the Societat Catalana de Matemàtiques, ISSN-e 2385-4227, Vol. 5, Nº. 1, 2020, págs. 23-32
• Idioma: inglés
• DOI: 10.2436/20.2002.02.20
• Enlaces
  • Texto completo
• Resumen
  • English

    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.

  • català

    En aquest treball estudiarem l'esquema de parells de matrius n×n amb commutador nul, pel que es conjectura que és reduït, Cohen–Macaulay i normal. Demostrarem que és regular en codimensió 3 però no en codimensió 4. També aportem resultats similars per a altres esquemes relacionats amb el nostre esquema original. En una segona part del treball estudiem les singularitats de l’esquema de parelles de matrius que commuten a partir de l'estudi dels corresponents esquemes de jets i altres invariants de singularitats com el log-canonical threshold.

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