# Birational geometry of moduli spaces of configurations of points on the line

@article{Bolognesi2017BirationalGO,
title={Birational geometry of moduli spaces of configurations of points on the line},
author={M. Bolognesi and Alex Massarenti},
journal={arXiv: Algebraic Geometry},
year={2017}
}
• Published 2017
• Mathematics
• arXiv: Algebraic Geometry
In this paper we study the geometry of GIT configurations of $n$ ordered points on $\mathbb{P}^1$ both from the the birational and the biregular viewpoint. In particular, we prove that any extremal ray of the Mori cone of effective curves of the quotient $(\mathbb{P}^1)^n//PGL(2)$, taken with the symmetric polarization, is generated by a one dimensional boundary stratum of the moduli space. Furthermore, we develop some technical machinery that we use to compute the canonical divisor and the… Expand
4 Citations
On the birational geometry of spaces of complete forms I: collineations and quadrics
Moduli spaces of complete collineations are wonderful compactifications of spaces of linear maps of maximal rank between two fixed vector spaces. We investigate the birational geometry of moduliExpand
On automorphisms of moduli spaces of parabolic vector bundles
• Mathematics
• 2019
Fix $n\geq 5$ general points $p_1, \dots, p_n\in\mathbb{P}^1$, and a weight vector $\mathcal{A} = (a_{1}, \dots, a_{n})$ of real numbers $0 \leq a_{i} \leq 1$. Consider the moduli spaceExpand
Complete symplectic quadrics and Kontsevich spaces of conics in Lagrangian Grassmannians
• Mathematics
• 2020
A wonderful compactification of an orbit under the action of a semi-simple and simply connected group is a smooth projective variety containing the orbit as a dense open subset, and where the addedExpand
Spherical blow-ups of Grassmannians and Mori dream spaces
• Mathematics
• 2018
Abstract In this paper we classify weak Fano varieties that can be obtained by blowing-up general points in prime Fano varieties. We also classify spherical blow-ups of Grassmannians in generalExpand

#### References

SHOWING 1-10 OF 90 REFERENCES
Towards the ample cone of \overline{}_{,}
• Mathematics
• 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 positiveExpand
On the birational geometry of spaces of complete forms I: collineations and quadrics
Moduli spaces of complete collineations are wonderful compactifications of spaces of linear maps of maximal rank between two fixed vector spaces. We investigate the birational geometry of moduliExpand
On the Automorphisms of Moduli Spaces of Curves
• Mathematics
• 2014
In the last years the biregular automorphisms of Deligne–Mumford’s and Hassett’s compactifications of the moduli space of n-pointed genus g smooth curves have been extensively studied by A. Bruno andExpand
Contractible Extremal Rays on \overline{M}_{0,n}
• Mathematics
• 1996
We consider the cones of curves and divisors on the moduli space of stable pointed rational curves,M_n, and on the quotient by the symmetric group, Q_n, which is a moduli space of pairs. We findExpand
On the Fano variety of linear spaces contained in two odd-dimensional quadrics
• Mathematics
• 2016
In this paper we describe the geometry of the 2m-dimensional Fano manifold G parametrizing (m-1)-planes in a smooth complete intersection Z of two quadric hypersurfaces in the complex projectiveExpand
Coherent systems and modular subvarieties of SU_C(r)
• Mathematics
• 2011
Let C be an algebraic smooth complex curve of genus g > 1. The object of this paper is the study of the birational structure of certain moduli spaces of vector bundles and of coherent systems on CExpand
Linear Systems and Quotients of Projective Space
A complete characterization of the categorical quotients of $({\mathbb P}^1)^n$ by the diagonal action of $\SL(2, {\mathbb C})$ with respect to any polarization is given by M. Polito, in ‘ $\SL(2,Expand The equations for the moduli space of$n$points on the line • Mathematics • 2009 A central question in invariant theory is that of determining the relations among invariants. Geometric invariant theory quotients come with a natural ample line bundle, and hence often a naturalExpand Factorization of point configurations, cyclic covers and conformal blocks • Mathematics • 2012 We describe a relation between the invariants of$n$ordered points in$P^d$and of points contained in a union of linear subspaces$P^{d1}\cup P^{d2} \subset P^d\$. This yields an attaching map forExpand
The Cone of Moving Curves on Algebraic Varieties
We give a new description of the closed cone of moving curves of a smooth Fano three- or fourfold by finitely many linear equations. In particular, the cone is polyhedral. The proof in the threefoldExpand