Noah GIANSIRACUSA, William Danny GILLAM

141111

On Kapranov's description of \overline{M}0,n as a Chow quotient

We provide a direct proof, valid in arbitrary characteristic, of the result originally proven by Kapranov over C that the Hilbert quotient (P1)n//HPGL2 and Chow quotient (P1)n//ChPGL2 are isomorphic to \overline{M}0,n. In both cases this is done by explicitly constructing the universal family of orbit closures and then showing that the induced morphism is an isomorphism onto its image. The proofs of these results in many ways reduce to the case n = 4; in an appendix we outline a formalism of this phenomenon relating to certain operads.
Anahtar Kelimeler:

Chow quotient, Hilbert quotient, moduli of curves, configuration of points

On Kapranov's description of \overline{M}0,n as a Chow quotient

We provide a direct proof, valid in arbitrary characteristic, of the result originally proven by Kapranov over C that the Hilbert quotient (P1)n//HPGL2 and Chow quotient (P1)n//ChPGL2 are isomorphic to \overline{M}0,n. In both cases this is done by explicitly constructing the universal family of orbit closures and then showing that the induced morphism is an isomorphism onto its image. The proofs of these results in many ways reduce to the case n = 4; in an appendix we outline a formalism of this phenomenon relating to certain operads.
Keywords:

Chow quotient, Hilbert quotient, moduli of curves, configuration of points,

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Turkish Journal of Mathematics-Cover
  • ISSN: 1300-0098
  • Yayın Aralığı: 6
  • Yayıncı: TÜBİTAK
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