The moduli space of n points on the line is cut out by simple quadrics when n is not six

Details The moduli space of n points on the line is cut out by simple quadrics when n is not six The moduli space of n points on the line is cut out by simple quadrics when n is not six

2006-07-16

arxiv.org/abs/math/0607372v1

Mathematics

Algebraic Geometry

25 pages, 16 figures

Scientific paper

A central question in invariant theory is that of determining the relations among invariants. Geometric invariant theory quotients come with a natural ample line bundle, and hence often a natural projective embedding. This question translates to determining the equations of the moduli space under this embedding. This note deals with one of the most classical quotients, the space of ordered points on the projective line. We show that under any linearization, this quotient is cut out (scheme-theoretically) by a particularly simple set of quadric relations, with the single exception of the Segre cubic threefold (the space of six points with equal weight). Unlike many facts in geometric invariant theory, these results (at least for the stable locus) are field-independent, and indeed work over the integers.

Affiliated with

Also associated with

No associations

Rating

The moduli space of n points on the line is cut out by simple quadrics when n is not six 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 The moduli space of n points on the line is cut out by simple quadrics when n is not six, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The moduli space of n points on the line is cut out by simple quadrics when n is not six will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-194736