Surfaces with p_g=q=3

2001/04/04 by Christopher D. Hacon, Rita Pardini, Hacon, Christopher D. +1
Computer Science · Engineering · Mathematics · #14J29 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Computational Geometry and Mesh Generation #FOS: Mathematics #Point processes and geometric inequalities #math.AG #msc:14J29

paper · pdf · doi:10.48550/arxiv.math/0104048

LaTeX2e, 9 pages

arxiv created 2001/04/04 · openalex publication_date 2001/04/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify minimal complex surfaces of general type with p_g=q=3. More precisely, we show that such a surface is either the symmetric product of a curve of genus 3 or a free \Z₂-quotient of the product of a curve of genus 2 and a curve of genus 3. Our main tools are the generic vanishing theorems of Green and Lazarsfeld and Fourier--Mukai transforms. The same result has been obtained independently at the same time by G. Pirola using different methods.

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