Segre's regularity bound for fat point schemes

• Uwe Nagel ^[1] ; Bill Trok ^[1]
  1. [1] University of Kentucky

     University of Kentucky

     Estados Unidos

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 20, Nº 1, 2020, págs. 217-237
• Idioma: inglés
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• Resumen

  • Motivated by questions in interpolation theory and on linear systems of rational varieties, one is interested in upper bounds for the CastelnuovoMumford regularity of arbitrary subschemes of fat points. An optimal upper bound, named after Segre, was conjectured by Trung and, independently, by Fatabbi and Lorenzini. It is shown that this conjecture is true. Furthermore, a generalized regularity bound is established that improves the Segre bound in some cases. Among the arguments is a new partition result for matroids