On the isotriviality of families of elliptic surfaces

1999/12/13 by Keiji Oguiso, Oguiso, Keiji, Eckart Viehweg +1 · 3 citations
Mathematics · #14J10 (Primary) 14D06 #14J27 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #math.AG #msc:14D06 #msc:14J10 #msc:14J27

paper · pdf · doi:10.48550/arxiv.math/9912100

24 pages, LaTeX, revised version

openalex publication_date 1999/12/13 · arxiv created 2000/01/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study non-isotrivial projective families of elliptic surfaces of Kodaira dimension one, over complex projective curves. If the base is an elliptic curve, we show that the family must have a singular fibre, and that over the projective line it must have at least three singular fibres. Similar results, for families of surfaces of general type, have been obtained by Migliorini and Kovács, and they are well-known for projective families of surfaces of Kodaira dimension zero. Revised version: We corrected some minor errors and ambiguities, and we completed the list of references.

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