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Bounded negativity, Miyaoka-Sakai inequality and elliptic curve configurations
- Publication Year :
- 2014
-
Abstract
- Similarly to the linear Harbourne constant recently defined, we study the elliptic $H$-constants of $\mathbb{P}^{2}$ 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.<br />Comment: Revised and shorter version
- Subjects :
- Mathematics - Algebraic Geometry
14J99
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1411.6996
- Document Type :
- Working Paper