Toric Degenerations of GIT Quotients, Chow Quotients, and $\bar{M_{0,n}$

Details Toric Degenerations of GIT Quotients, Chow Quotients, and $\bar{M_{0,n}$ Toric Degenerations of GIT Quotients, Chow Quotients, and $\bar{M_{0,n}$

2006-07-31

arxiv.org/abs/math/0607824v1

Mathematics

Algebraic Geometry

8 pages

Scientific paper

We show that the moduli space of stable n-pointed rational curves can be flatly degenerated to a projective toric variety. We arrive at this by showing that the Chow quotients of the Grassmannians admit toric degenerations, which in turn, follows from a theorem that we prove for toric degenerations of more general Chow quotients. Along the way, we also argued that GIT quotient of a flat family is again flat. In particular, all GIT quotients of flag varieties by maximal tori can be flatly degenerated to projective toric varieties ([9] and [12]).

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