Toric Degenerations of GIT Quotients, Chow Quotients, and M0,n

6 Toric Degenerations of Git Quotients , Chow Quotients

The moduli spaceM0,n plays important roles in algebraic geometry and theoretical physics. Yet, some basic properties of M 0,n still remain open. For example, M0,n is rational and nearly toric (that is, it contains a toric variety as a Zariski open subset), but it is not a toric variety itself starting from dimension 2 (n ≥ 5). So, a basic question is: Can it be degenerated flatly to a projectiv...

Chow Quotients and Euler - Chow Series

Given a projective algebraic variety X, let p(X) denote the monoid of eeective algebraic equivalence classes of eeective algebraic cycles on X. The p-th Euler-Chow series of X is an element in the formal monoid-ring Z p(X)] ] deened in terms of Euler characteristics of the Chow varieties Cp;; (X) of X, with 2 p(X). We provide a systematic treatment of such series, and give projective bundle for...

Toric quotients and flips

As my contribution to these proceedings, I will discuss the geometric invariant theory quotients of toric varieties. Specifically, I will show that quotients of the same problem with respect to different linearizations are typically related by a sequence of flips (or more precisely, log flips) in the sense of Mori, which in the quasi-smooth case can be characterized quite precisely. This seems ...

Quotients of Divisorial Toric

Chow Quotients of Grassmannians Ii

1.0 Properties of M0,n ⊂ M0,n. (1) M0,n has a natural moduli interpretation, namely it is the moduli space of stable n-pointed rational curves. (2) Given power series f1(z), . . . , fn(z) which we think of as a one parameter family in M0,n one can ask: What is the limiting stable n-pointed rational curve in M0,n as z → 0 ? There is a beautiful answer, due to Kapranov [Kapranov93a], in terms of ...