Conformal blocks and rational normal curves

Details Conformal blocks and rational normal curves Conformal blocks and rational normal curves

2010-12-21

arxiv.org/abs/1012.4835v2

Mathematics

Algebraic Geometry

17 pages, 1 figure; added result that map to Chow quotient is an isomorphism and section on self-association; additional minor

Scientific paper

We prove that the Chow quotient parametrizing configurations of n points in P^d which generically lie on a rational normal curve is isomorphic to M_{0,n}, generalizing the well-known d = 1 result of Kapranov. In particular, M_{0,n} admits birational morphisms to all the corresponding geometric invariant theory (GIT) quotients. For symmetric linearizations the polarization on each GIT quotient pulls back to a divisor that spans the same extremal ray in the symmetric nef cone of M_{0,n} as a conformal blocks line bundle. A symmetry in conformal blocks implies a duality of point-configurations that comes from Gale duality and generalizes a result of Goppa in algebraic coding theory. In a suitable sense, M_{0,2m} is fixed pointwise by the Gale transform when d=m-1 so stable curves correspond to self-associated configurations.

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