Bounded negativity, Miyaoka-Sakai inequality and elliptic curve configurations

2014/11/25 by Roulleau, Xavier
#14J99 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1411.6996

Abstract

Similarly to the linear Harbourne constant recently defined, we study the elliptic H-constants of ℙ² and Abelian surfaces. We exhibit configurations of smooth plane cubic curves whose Harbourne index is arbitrarily close to -4. As a Corollary, we obtain that the global H-constant of any surface X is less or equal to -4. Related to these problems, we moreover give a new inequality for the number and multiplicities of singularities of elliptic curves arrangements on Abelian surfaces, inequality which has a close similarity to the one of Hirzebruch for arrangements of lines in the plane.

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