Standard isotrivial fibrations with pg=q=1

2007/03/31 by Francesco Polizzi
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Combinatorics #Fibration #Geometric and Algebraic Topology #Gravitational singularity #Homotopy #Mathematical analysis #Mathematics #Pure mathematics #Scroll #Theology #Type (biology) #math.AG #math.GR #msc:14J29 #msc:14Q99 #msc:20F65

paper · pdf · doi:10.1016/j.jalgebra.2008.10.028

published as J. Algebra 321 (2009), 1600-1631 · 31 pages. Final version, to appear in J. Algebra

arxiv created 2008/08/03 · openalex publication_date 2009/01/20 · arxiv updated 2014/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

A smooth, projective surface S of general type is said to be a standard isotrivial fibration if there exist a finite group G which acts faithfully on two smooth projective curves C and F so that S is isomorphic to the minimal desingularization of T:=(C × F)/G. If T is smooth then S=T is called a quasi-bundle. In this paper we classify the standard isotrivial fibrations with p_g=q=1 which are not quasi-bundles, assuming that all the singularities of T are rational double points. As a by-product, we provide several new examples of minimal surfaces of general type with p_g=q=1 and K_S²=4,6.

Citations

• Complex Algebraic Surfaces
• Surfaces of general type with 𝑝_𝑔=𝑞=1,𝐾²=8 and bicanonical map of degree 2
• The classification of surfaces with p_g = q = 0 isogenous to a product of curves