Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Conformal blocks and rational normal curves


Author: Noah Giansiracusa
Journal: J. Algebraic Geom. 22 (2013), 773-793
DOI: https://doi.org/10.1090/S1056-3911-2013-00601-3
Published electronically: June 18, 2013
MathSciNet review: 3084722
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Abstract | References | Additional Information

Abstract: We prove that the Chow quotient parameterizing configurations of $ n$ points in $ \mathbb{P}^d$ which generically lie on a rational normal curve is isomorphic to $ \overline {\mathcal {M}}_{0,n}$, generalizing the well-known $ d=1$ result of Kapranov. In particular, $ \overline {\mathcal {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 {\mathcal {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 {\mathcal {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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Noah Giansiracusa
Affiliation: Department of Mathematics, Brown University, Providence, Rhode Island 02912
Address at time of publication: Department of Mathematics, University of California, Berkeley, Berkeley, California 94720
Email: noahgian@math.brown.edu, noahgian@math.berkeley.edu

DOI: https://doi.org/10.1090/S1056-3911-2013-00601-3
Received by editor(s): January 16, 2011
Received by editor(s) in revised form: April 11, 2011
Published electronically: June 18, 2013
Additional Notes: The author was partially supported by funds from NSF DMS-0901278.
Communicated by: Michel Brion
Article copyright: © Copyright 2013 University Press, Inc.
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society