Surfaces with pg=q=3
Abstract
We classify minimal complex surfaces of general type with pg=q=3. More precisely, we show that such a surface is either the symmetric product of a curve of genus 3 or a free 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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