<Posters>Quasi-étale covers of Du Val del Pezzo surfaces and Zariski dense exceptional sets in dimension 2

Abstract

In [1, 2], we study surfaces with Zariski dense exceptional sets in Manin's conjecture. By an MMP-type argument in [3], this reduces to the study of weak del Pezzo surfaces with the anticanonical polarization. In [1], we give examples of del Pezzo surfaces of degree 1 and Picard rank 1 with dense exceptional sets. In [2], we classify possibilities of such examples in the case of weak del Pezzo surfaces. The existence of such examples were known in dimension ≥3, but were unexpected in dimension 2. We focus on [2] in this poster.