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Towards the ample cone of \overline{}_{,}

- A. Gibney, S. Keel, I. Morrison
- Mathematics
- 27 June 2000

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 positive… Expand

On finite generation of the section ring of the determinant of cohomology line bundle

- P. Belkale, A. Gibney
- Mathematics
- 28 June 2016

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 the… Expand

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 to… Expand

Pointed trees of projective spaces

- Linda Chen, A. Gibney, D. Krashen
- Mathematics
- 14 May 2005

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 the… Expand

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 nodes… Expand

Equations for Chow and Hilbert quotients

- A. Gibney, D. Maclagan
- Mathematics
- 12 July 2007

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 geometric… Expand

Lower and upper bounds for nef cones

- A. Gibney, D. Maclagan
- Mathematics
- 1 September 2010

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 using… Expand

Compact Moduli Spaces and Vector Bundles

- V. Alexeev, A. Gibney, E. Izadi, J. Kollár, E. Looijenga
- Mathematics
- 2012

Numerical criteria for divisors on M g to be ample

- A. Gibney
- 2009

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

Surveys on Recent Developments in Algebraic Geometry

- Izzet Coskun, T. Fernex, A. Gibney
- Mathematics
- 12 July 2017

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