An algebraic proof of Iitaka's Conjecture C_2,1

2001/03/30 by Markus Wessler, Wessler, Markus
Mathematics · #14D06 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #math.AG #msc:14D06

paper · pdf · doi:10.48550/arxiv.math/0103225

7 pages

arxiv created 2001/03/30 · openalex publication_date 2001/03/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a proof of Iitaka's Conjecture C_2,1 using only elementary methods from algebraic geometry. The main point is that, given a non-isotrivial and relatively minimal family f : X → B, where X is a surface and B is a curve, both smooth and projective, we show that the direct image of the relatively canonical sheaf has strictly positive degree.

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