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Towards the ample cone of \overline{}_{,}
In this paper we study the ample cone of the moduli space $\mgn$ of stable $n$-pointed curves of genus $g$. Our motivating conjecture is that a divisor on $\mgn$ is ample iff it has positiveExpand
On finite generation of the section ring of the determinant of cohomology line bundle
For $C$ a stable curve of arithmetic genus $g\ge 2$, and $\mathcal{D}$ the determinant of cohomology line bundle on $\operatorname{Bun}_{\operatorname{SL}(r)}(C)$, we show the section ring for theExpand
The mori cones of moduli spaces of pointed curves of small genus
We compute the Mori cones of the moduli spaces M g,n of n pointed stable curves of genus g, when g and n are relatively small. For instance we show that for g < 14 every curve in Mg is equivalent toExpand
Pointed trees of projective spaces
We introduce a smooth projective variety $T_{d,n}$ which compactifies the space of configurations of $n$ distinct points on affine $d$-space modulo translation and homothety. The points in theExpand
Numerical criteria for divisors on $\overline {M}_{g}$ to be ample
  • A. Gibney
  • Mathematics
  • Compositio Mathematica
  • 3 December 2003
Abstract The moduli space $\M _{g,n}$ of n-pointed stable curves of genus g is stratified by the topological type of the curves being parameterized: the closure of the locus of curves with k nodesExpand
Equations for Chow and Hilbert quotients
We give explicit equations for the Chow and Hilbert quotients of a projective scheme X by the action of an algebraic torus T in an auxiliary toric variety. As a consequence we provide geometricExpand
Lower and upper bounds for nef cones
The nef cone of a projective variety Y is an important and often elusive invariant. In this paper we construct two polyhedral lower bounds and one polyhedral upper bound for the nef cone of Y usingExpand
Numerical criteria for divisors on M g to be ample
The moduli space Mg,n of n-pointed stable curves of genus g is stratified by the topological type of the curves being parameterized: the closure of the locus of curves with k nodes has codimension k.Expand
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