Unbounded negativity on rational surfaces in positive characteristic

Journal für die reine und angewandte Mathematik (Crelles Journal), vol. 2022, pp. 217–226

Abstract

Abstract We give explicit blowups of the projective plane in positive characteristic that contain smooth rational curves of arbitrarily negative self-intersection, showing that the Bounded Negativity Conjecture fails even for rational surfaces in positive characteristic. As a consequence, we show that any surface in positive characteristic admits a birational model failing the Bounded Negativity Conjecture.

Authors 1

1. Remy van Dobben de Bruyn Aachen Mathematisch Instituut

   Leiden University

   Affiliation as printed

   Mathematisch Instituut , Universiteit Leiden , Niels Bohrweg 1 , 2333 CA Leiden , The Netherlands