Blow-up algebras of secant varieties of rational normal scrolls

• Lin, Kuei-Nuan ^[2] ; Shen, Yi-Huang ^[1]
  1. [1] University of Science and Technology of China

     University of Science and Technology of China

     China

     
  2. [2] Department of Mathematics, The Penn State University, McKeesport, PA, 15132, USA
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 74, Fasc. 1, 2023, págs. 247-278
• Idioma: inglés
• DOI: 10.1007/s13348-021-00345-2
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• Resumen

  • In this paper, we are mainly concerned with the blow-up algebras of the secant varieties of balanced rational normal scrolls. In the first part, we give implicit defining equations of their associated Rees algebras and fiber cones. Consequently, we can tell that the fiber cones are Cohen–Macaulay normal domains. Meanwhile, these fiber cones have rational singularities in characteristic zero, and are F-rational in positive characteristic. The Gorensteinness of the fiber cones can also be characterized. In the second part, we compute the Castelnuovo–Mumford regularities and aa-invariants of the fiber cones. We also present the reduction numbers of the ideals defined by the secant varieties.