In mathematics, a Castelnuovo surface is a surface of general type such that the canonical bundle is very ample and such that c<sub>1</sub><sup>2</sup> = 3p<sub>g</sub> − 7. Guido Castelnuovo proved that if the canonical bundle is very ample for a surface of general type then c<sub>1</sub><sup>2</sup> âÂÂ¥ 3p<sub>g</sub> − 7.