Guardado en:
Detalles Bibliográficos
Autores principales: Adiprasito, Karim, Björner, Anders, Hakavuori, Joel, Margaritis, Minas, Welker, Volkmar
Formato: Preprint
Publicado: 2024
Materias:
Acceso en línea:https://arxiv.org/abs/2404.16643
Etiquetas: Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
Tabla de Contenidos:
  • We show that the maximal shifts in the minimal free resolution of the quotients of a polynomial ring by a monomial ideal are subadditive as a function of the homological degree. This answers a question that has received some attention in recent years. To do so, we define and study a new model for the homology of posets, given by the so called synor complex. We also introduce an Eilenberg-Zilber type shuffle product on the simplicial chain complex of lattices. Combining these concepts we prove that the existence of a non-zero homology class for a lattice forces certain non-zero homology classes in lower intervals. This result then translates into properties of the minimal free resolution. In particular, it implies a generalization of the original question.