On surfaces with p_g=2, q=1 and non-birational bicanonical map

2002/03/01 by Ciro Ciliberto, Ciliberto, Ciro, Margarida Mendes Lopes +1 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AG

paper · pdf · doi:10.48550/arxiv.math/0203007

Latex 2e, 10 pages. To appear in the Proceedings of the Conference in memory of Paolo Francia, Genova, September 2001

arxiv created 2002/03/01 · openalex publication_date 2002/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present note we show that any surface of general type with p_g=2,q=1 and non-birational bicanonical map has a pencil of curves of genus 2. Combining this result with previous ones, one obtains thatan irregular surface S of general type with χ(S)≥ 2 and non-birational bicanonical map has a pencil of curves of genus 2.

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• On surfaces with p_g=q=1 and non-ruled bicanonical involution

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