Questions and conjectures on extremal Hilbert series

• Ralf Fröberg ^[1] ; Samuel Lundqvist ^[1]
  1. [1] Stockholm University

     Stockholm University

     Suecia

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 59, Nº. 2, 2018, págs. 415-429
• Idioma: inglés
• DOI: 10.33044/revuma.v59n2a10
• Enlaces
  • Texto completo (pdf)
• Resumen

  • Given an ideal of forms in an algebra (polynomial ring, tensor algebra, exterior algebra, Lie algebra, bigraded polynomial ring), we consider the Hilbert series of the factor ring. We concentrate on the minimal Hilbert series, which is achieved when the forms are generic. In the polynomial ring we also consider the opposite case of maximal series. This is mainly a survey article, but we give a lot of problems and conjectures. The only novel results concern the maximal series in the polynomial ring.