The Manin–Peyre Conjecture for Two Quintic del Pezzo Surfaces with Singularity Types A₃ and A₄

Abstract

The Manin–Peyre conjecture is established for two split singular quintic del Pezzo surfaces with singularity types A₃ and A₄. We use a general and different method, which can generalise to other situations, from Chambert-Loir and Tschinkel [Invent. Math., 2002, 148: 421–452].

Keywords

Manin–Peyre conjecture / del Pezzo surfaces / universal torsors / rational points / 11D45 / 11G25 / 11G50 / 11P55 / 14G05

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