The cone of type A, level 1, conformal blocks divisors

Noah Giansiracusa, Angela Gibney

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

We prove that the type A, level 1, conformal blocks divisors on M 0,n span a finitely generated, full-dimensional subcone of the nef cone. Each such divisor induces a morphism from M 0,n, and we identify its image as a GIT quotient parameterizing configurations of points supported on a flat limit of Veronese curves. We show how scaling GIT linearizations gives geometric meaning to certain identities among conformal blocks divisor classes. This also gives modular interpretations, in the form of GIT constructions, to the images of the hyperelliptic and cyclic trigonal loci in M g under an extended Torelli map.

Original languageEnglish (US)
Pages (from-to)798-814
Number of pages17
JournalAdvances in Mathematics
Volume231
Issue number2
DOIs
StatePublished - Oct 1 2012
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Conformal blocks
  • GIT
  • Moduli of curves
  • Nef cone

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