Counting points with Riemann-Roch formulas

• Jorge Martín-Morales ^[1]
  1. [1] Universidad de Zaragoza

     Universidad de Zaragoza

     Zaragoza, España

     
• Localización: Revista de la Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza, ISSN 0370-3207, Nº. 78, 2023, págs. 7-40
• Idioma: inglés
• Enlaces
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• Resumen

  • We provide an algorithm for computing the number of integral points lying in certain triangles that do not have integral vertices. We use techniques from Algebraic Geometry such as the Riemann-Roch formula for weighted projective planes and resolution of singularities. We analyze the complexity of the method and show that the worst case is given by the Fibonacci sequence. At the end of the manuscript a concrete example is developed in detail where the interplay with other invariants of singularity theory is also treated.