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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Additional Information

**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

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.