Conformal blocks and rational normal curves
By Noah Giansiracusa. 2010
51 citations recorded by the source corpus.
We prove that the Chow quotient parametrizing configurations of n points in $\mathbb{P}^d$ which generically lie on a rational normal curve is isomorphic to $\overline{M}_{0,n}$, generalizing the well-known $d = 1$ result of Kapranov. In particular, $\overline{M}_{0,n}$ 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 $\overline{M}_{0,n}$ 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, $\overline{M}_{0,2m}$ is fixed pointwise by the Gale transform when $d=m-1$ so stable curves correspond to self-associated configurations.
Subfields: Computational Mechanics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/c2abb27f4f9257a85beb85a535f1b59bd2c0301a
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Citations in the corpus
- The cone of type A, level one conformal blocks divisors (2011, methodology): “orphisms factor as the composition of a forgetful map with a birational morphism to a GIT quotient parameterizing configurations of points that lie on a flat limit of Veronese curves— what is called in [Gia11] a quasi-Veronesecurve. This birational map further factors through a Hassett moduli space M0”
- Chern classes of conformal blocks (2009, background): “ reappear here for suitable choices of weights and it seems likely that all level 1 conformal blocks have a GIT interpretation. This has been shown to be true for symmetric weights by N. Giansiracusa [9]. The case of sp2ℓ is also noteworthy; the bundles of conformal blocks for these Lie algebras at ”