Del Pezzo Moduli via Root Systems

Abstract

Coble defined in his 1929 treatise invariants for cubic surfaces and quartic curves. We reinterpret these in terms of the root systems of type E6 and E7 that are naturally associated to these varieties, thereby giving some of his results a more intrinsic treatment. Our discussion is uniform for all Del Pezzo surfaces of degree 2,3,4 and 5.