Non-singular cubic surfaces with star points. (Q1862710)

A star point on a smooth cubic surface is a point where three of the twenty-seven lines meet. It is known that there are at most 18 star points. The author studies the filtration of the space of smooth cubic surfaces \(\mathbb{P}(H^0(\mathbb{P}^3, \mathcal O(3)))\setminus \Delta\) by the loci \(H_k\) of cubics having at most \(k\) star points. The geometry of \(H_k\) is described in terms of configuration of six points in \(\mathbb{P}^2\) corresponding to the cubic surface. Several results concerning the irreducible components of \(H_k\) are announced [cf. Kodai Math. J. 27, No.1, 57--73 (2004; Zbl 1068.14042)].