Parametrizing Del Pezzo surfaces of degree 8 using Lie algebras

2005/12/20 by Willem A. de Graaf, Jana Pílniková, Jana Ṕılniková +4
Computer Science · Mathematics · #14Q10 (primary) #17B45 (secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14Q10 #msc:17B45

paper · pdf · doi:10.48550/arxiv.math/0512477

22 pages

arxiv created 2005/12/20 · openalex publication_date 2005/12/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a Del Pezzo surface of degree 8 given over the rationals we decide whether there is a rational parametrization of the surface and construct one in the affirmative case. We define and use the Lie algebra of the surface to reach the aim. The algorithm has been implemented in Magma.

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