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- W2239272252 abstract "We introduce spaces which generically parametrize con?gurations of n points on a degree d rational normal curve. The quotients of these spaces by SL(d+1) are all birational to the moduli space M_{0,n} of stable n-pointed rational curves. In the case of pointed conics (d=2) we characterize stability in the sense of geometric invariant theory (GIT). The space of e?ective linearizations is described in terms of hypersimplices. There is a natural wall in this space: on one side semistable nodal conics occur, and on the other all the quotients are isomorphic to P1^n//SL(2). These latter quotients receive a morphism from M_{0,n} by a result of Kapranov, and our main result is that the quotients on the other side of the wall also receive such a morphism. For arbitrary degree d we study the quotients which parametrize the points supported on the curve rather than the pointed curve itself. We prove that these Chow quotients are isomorphic to M_{0,n}, generalizing Kapranov�s d=1 result. In particular, M_{0,n} admits birational morphisms to all the corresponding 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-con?gurations that we show comes from Gale duality and generalizes a result of Goppa in algebraic coding theory. In a suitable sense, M_{0,2m} is ?xed pointwise by the Gale transform when d=m-1 so stable curves correspond to self-associated con?gurations." @default.
- W2239272252 created "2016-06-24" @default.
- W2239272252 creator A5033650471 @default.
- W2239272252 date "2011-01-01" @default.
- W2239272252 modified "2023-09-23" @default.
- W2239272252 title "Birational Models from Rational Normal Curves" @default.
- W2239272252 hasPublicationYear "2011" @default.
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