Noah GIANSIRACUSA, William Danny GILLAM

134100

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,

Turkish Journal of Mathematics-Cover

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

Arşiv

Sayıdaki Diğer Makaleler

Oscillation of second order differential equations with mixed nonlinearities

Zhiting XU, Aijun CHENG

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

Noah GIANSIRACUSA, William Danny GILLAM

Half-lightlike submanifolds with planar normal sections in R24

Feyza Esra ERDOĞAN, Rıfat GÜNEŞ, Bayram ŞAHİN

Some rings for which the cosingular submodule of every module is a direct summand

Derya TÜTÜNCÜ KESKIN, Rachid TRIBAK, Nil ERTAS ORHAN, Patrick SMITH F.

On semiparallel anti-invariant submanifolds of generalized Sasakian space forms

Cihan ÖZGÜR, Fatma GÜRLER, Cengizhan MURATHAN

Degenerate Hopf bifurcations, hidden attractors, and control in the extended Sprott E system with only one stable equilibrium

Anping LIU, Zhouchao WEI, Irene MOROZ

On Joachimsthal's theorems in Riemann Otsuki space R − O3

Mehmet BEKTAŞ, Münevver YILMAZ YILDIRIM

Continuity of Wigner-type operators on Lorentz spaces and Lorentz mixed normed modulation spaces

Ayşe SANDIKÇI

Almost contact metric submersions and symplectic manifolds

Augustin BATUBENGE, Tshikunguila TSHIKUNA-MATAMBA

Regular poles for the p-adic group GSp4

Yusuf DANIŞMAN