an:06984852
Zbl 1404.14014
Pokora, Piotr; Roulleau, Xavier; Szemberg, Tomasz
Bounded negativity, Harbourne constants and transversal arrangements of curves
EN
Ann. Inst. Fourier 67, No. 6, 2719-2735 (2017).
00423264
2017
j
14C20 14J70
curve arrangements; algebraic surfaces; Miyaoka inequality; blow-ups; negativity curves; bounded negativity conjecture
The paper under review is devoted to birational geometry of complex algebraic surfaces. It is motivated by the Bounded Negativity Conjecture, which stiputales that for every smooth complex projective surface \(X\), there exists a number \(b(X)\), which bounds the self-intersection of an arbitrary reduced divisor on \(X\) from below (it is clear that no such upper bound can exist). The authors provide lower bound on the self-intersection of certain classes of divisors on blow-ups of surfaces with non-negative Kodaira dimension (Theorem A) and on blow-ups of \(\mathbb{P}^2\) (Theorem B).
The paper is to a far extent self-contained, the discussion is streamlined and the arguments are transparent, even if ocassionally technical. The main tools are variants of the Miyaoka-Yau inequality and the analysis of some numerical invariants, here Harbourne constants.
Justyna Szpond (Krak??w)