Negative curves on special rational surfaces

2019/09/12 by Marcin Dumnicki, Dumnicki, Marcin, Łucja Farnik +11
Mathematics · #14C20 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1909.05899

openalex publication_date 2019/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study negative curves on surfaces obtained by blowing up special configurations of points in the complex projective palne. Our main results concern the following configurations: very general points on a cubic, 3-torsion points on an elliptic curve and nine Fermat points. As a consequence of our analysis, we also show that the Bounded Negativity Conjecture holds for the surfaces we consider. The note contains also some problems for future attention.

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