Surfaces with $p_g=q=3$

Details Surfaces with $p_g=q=3$ Surfaces with $p_g=q=3$

2001-04-04

arxiv.org/abs/math/0104048v1

Mathematics

Algebraic Geometry

LaTeX2e, 9 pages

Scientific paper

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 $\Z_2-$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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