2004/12/02 by Matthias Schuett, Schuett, Matthias
Arts and Humanities · Mathematics · #14J27 #14J28 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #French Historical and Cultural Studies #North African History and Literature #math.AG #msc:14J27 #msc:14J28
paper · pdf · doi:10.48550/arxiv.math/0412049
27 pages, 33 figures, 2 tables; major revision: Third version has minor typos corrected, exposition improved and references updated or added ([BM], [Kl], [N],[S])
openalex publication_date 2004/12/02 · arxiv created 2006/05/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is concerned with the construction of extremal elliptic K3 surfaces. It gives a complete treatment of those fibrations which can be derived from rational elliptic surfaces by easy manipulations of their Weierstrass equations. In particular, this approach enables us to find explicit equations for 38 semi-stable extremal elliptic K3 fibrations, 32 of which are indeed defined over the rationals. They are realized as pull-back of non-semi-stable extremal rational elliptic surfaces via base change. This is related to work of J. Top and N. Yui which exhibited the same procedure for the semi-stable extremal rational elliptic surfaces.