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Abstract
Consider the projective coordinate ring of the Geometric Invariant Theory (GIT) quotient (ℙ1)
n
//SL(2), with the usual linearization, where n is even. In 1894, Kempe proved that this ring is generated in degree one. In [Citation2] we showed that, over ℚ, the relations between degree one invariants are generated by a class of quadratic relations—the simplest binomial relations—with the exception of n = 6, where there is a single cubic relation. The purpose of this article is to show that these results hold over , and to suggest why they may be true over
.
ACKNOWLEDGMENTS
We thank Chris Manon and Lawrence O'Neil for some helpful discussions.
B. Howard was supported by NSF fellowship DMS-0703674. J. Millson was supported by the NSF grant DMS-0405606, the NSF FRG grant DMS-0554254 and the Simons Foundation. A. Snowden was partially supported by NSF fellowship DMS-0902661. R. Vakil was partially supported by NSF grant DMS-0801196.
Notes
Communicated by L. Ein.