7 papers · 1 filter
An explicit wall crossing for the moduli space of hyperplane arrangements
Patricio Gallardo, Luca Schaffler
The moduli space of hyperplanes in projective space has a family of geometric and modular compactifications that parametrize stable hyperplane arrangements with respect to a weight…
Computation of GIT quotients of semisimple groups
Patricio Gallardo, Jesus Martinez-Garcia, Han-Bom Moon +1
We describe three algorithms to determine the stable, semistable, and torus-polystable loci of the GIT quotient of a projective variety by a reductive group. The algorithms are eff…
Higher-dimensional Losev-Manin spaces and their geometry
Patricio Gallardo, Javier González-Anaya, José Luis González +1
The classical Losev-Manin space is a toric compactification of the moduli space of points in the affine line modulo translation and scaling. Motivated by this, we study its hig…
Algebraic and analytic compactifications of moduli spaces
Patricio Gallardo, Matt Kerr
In this expository note, we offer an overview of the relationship between Hodge-theoretic and geometric compactifications of moduli spaces of algebraic varieties.
The Fulton-MacPherson compactification is not a Mori dream space
Patricio Gallardo, José Luis González, Evangelos Routis
We show that the Fulton-MacPherson compactification of the configuration space of distinct labeled points in certain varieties of arbitrary dimension , including projective…
Geometric interpretation of toroidal compactifications of moduli of points in the line and cubic surfaces
Patricio Gallardo, Matt Kerr, Luca Schaffler
It is known that some GIT compactifications associated to moduli spaces of either points in the projective line or cubic surfaces are isomorphic to Baily-Borel compactifications of…