A Complex Ball Uniformization of the Moduli Space of Cubic Surfaces Via Periods of K3 Surfaces

Details A Complex Ball Uniformization of the Moduli Space of Cubic Surfaces Via Periods of K3 Surfaces A Complex Ball Uniformization of the Moduli Space of Cubic Surfaces Via Periods of K3 Surfaces

2003-10-21

arxiv.org/abs/math/0310342v1

Mathematics

Algebraic Geometry

47 pages, LaTeX

Scientific paper

In this paper we show that the moduli space of nodal cubic surfaces is isomorphic to a quotient of a 4-dimensional complex ball by an arithmetic subgroup of the unitary group. This complex ball uniformization uses the periods of certain K3 surfaces which are naturally associated to cubic surfaces. A similar uniformization is given for the covers of the moduli space corresponding to geometric markings of the Picard group or to the choice of a line on the surface. We also give a detailed description of the boundary components corresponding to singular surfaces.

Affiliated with

Also associated with

No associations

Rating

A Complex Ball Uniformization of the Moduli Space of Cubic Surfaces Via Periods of K3 Surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Complex Ball Uniformization of the Moduli Space of Cubic Surfaces Via Periods of K3 Surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Complex Ball Uniformization of the Moduli Space of Cubic Surfaces Via Periods of K3 Surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-510192