Curve configurations in the projective plane and their characteristic numbers
Volume 116 / 2018
Banach Center Publications 116 (2018), 63-76
MSC: Primary 14C20; Secondary 52C35.
DOI: 10.4064/bc116-4
Abstract
In this paper/survey, we study the concept of characteristic numbers and Chern slopes in the context of curve configurations in the real and complex projective plane. We show that some extremal line configurations inherit the same asymptotic invariants, namely asymptotic Chern slopes and asymptotic Harbourne constants, which sheds some light on relations between the bounded negativity conjecture and the geography problem for surfaces of general type. We discuss some properties of Kummer extensions, especially in the context of ball-quotients. Moreover, we prove that for a certain class of smooth curve configurations in the projective plane their characteristic numbers are bounded by $8/3$.
