Stability of Cubic 3-folds

Abstract

Hilbert's idea of null forms appeared again as the stability and plays an important role in constructing the moduli space and its compactification in Geometric Invariant Theory of Mumford By virtue of the numerical criterion, one can determine the stable objects explicitly. For example, Hilbert proved the following. (See [3, 19] and [8, p15].) THEOREM. Let S be a cubic surface in the projective space P 3 .