Chow Quotients of Grassmannians Ii Sean Keel and Jenia Tevelev

Geometry of Chow Quotients of Grassmannians

We consider Kapranov’s Chow quotient compactification of the moduli space of ordered n-tuples of hyperplanes in P r−1 in linear general position. For r = 2, this is canonically identified with the Grothendieck-Knudsen compactification of M0,n which has, among others, the following nice properties: (1) modular meaning: stable pointed rational curves; (2) canonical description of limits of one-pa...

Compactifications of Subvarieties of Tori

We study compactifications of subvarieties of algebraic tori defined by imposing a sufficiently fine polyhedral structure on their non-archimedean amoebas. These compactifications have many nice properties, for example any k boundary divisors intersect in codimension k. We consider some examples including M0,n ⊂ M0,n (and more generally log canonical models of complements of hyperplane arrangem...

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 ...

Sean Keel And

We show that the log canonical bundle, κ, of M0,n is very ample, show the homogeneous coordinate ring is Koszul, and give a nice set of rank 4 quadratic generators for the homogeneous ideal: The embedding is equivariant for the symmetric group, and the image lies on many Segre embedded copies of P×· · ·×P, permuted by the symmetric group. The homogeneous ideal of M0,n is the sum of the homogene...

Graduate Algebra: Numbers, Equations, Symmetries