On a constant arising in Manin's conjecture for Del Pezzo surfaces

• Autores: Ulrich Derenthal
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 14, Nº 3, 2007, págs. 481-489
• Idioma: inglés
• DOI: 10.4310/mrl.2007.v14.n3.a12
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• Resumen

  • For split smooth Del Pezzo surfaces, we analyse the structure of the effective cone and prove a recursive formula for the value of $\alpha$, appearing in the leading constant as predicted by Peyre of Manin's conjecture on the number of rational points of bounded height on the surface. Furthermore, we calculate $\alpha$ for all singular Del Pezzo surfaces of degree $\ge 3$.