Positivity of tropical multidegrees

• Xiang He ^[1]
  1. [1] Tsinghua University

     Tsinghua University

     China

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 3, 2024, págs. 1-14
• Idioma: inglés
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• Resumen

  • Let Ґ a tropical variety in Rm = Rm1 ×···× Rmk . We show that, under a certain condition, the positivity of the stable intersection of with certain tropical varieties pulled back from each Rmi is governed by the dimensions of the images of under all possible projections from Rm. As an application, we give a tropical proof of the criterion of the positivity of the multidegrees of a closed subscheme of a multi-projective space, carried out in the paper Castillo et al. (Adv Math 374:107382, 2020).