The distribution of Weierstrass points on a tropical curve

• David Harry Richman ^[1]
  1. [1] University of Washington

     University of Washington

     Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 2, 2024, págs. 1-48
• Idioma: inglés
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• Resumen

  • We show that on a metric graph of genus g, a divisor of degree n generically has g(n − g + 1) Weierstrass points. For a sequence of generic divisors on a metric graph whose degrees grow to infinity, we show that the associated Weierstrass points become distributed according to the Zhang canonical measure. In other words, the limiting distribution is determined by effective resistances on the metric graph. This distribution result has an analogue for complex algebraic curves, due to Neeman, and for curves over non-Archimedean fields, due to Amini.