2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61230We 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.LaTeX2e, 9 pagesAlgebraic Geometry14J29text