Fulton's conjecture on the ample cone of the moduli space
of n-pointed curves, and related problems and computational tools
Abstract: The moduli space bar{M_g,n) of stable pointed curves of genus
g has a stratification in which codimension k-strata are the irreducible
components of the locus parametrizing curves with at least k singularities.
It is known that any divisor is linearly equivalent to a sum of codimension-
1 strata and that dimension 1 subvarieties are equivalent to to sums of 1-
strata. Fulton's conjecture says that an effective sum of curves is
actually equivalent to an EFFECTIVE sum of 1-strata. This would give us a
nice combinatorial description of the ample cone. Fulton's conjecture for
arbitrary genus reduces to a similar statement in M_0,n+g. In this seminar,
we will investigate M_0,n and it's relevant cones and look at various
results related to Fulton's conjecture. Later in the semester, we will look
at algorithmic methods in convex geometry which have applications to the
results above.
The First talk will focus on definitions and finding an explicit blow-up
representation for M_0,n. The Blowup representation in turn leads to a nice
description of the chow ring.