5 papers
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…
On the neighborliness of dual flow polytopes of quivers
Patricio Gallardo, Daniel Mckenzie
In this note we investigate under which conditions the dual of the flow polytope (henceforth referred to as the `dual flow polytope') of a quiver is k-neighborly, for generic weigh…
Applications of the moduli continuity method to log K-stable pairs
Patricio Gallardo, Jesus Martinez-Garcia, Cristiano Spotti
The 'moduli continuity method' permits an explicit algebraisation of the Gromov-Hausdorff compactification of Kähler-Einstein metrics on Fano manifolds in some fundamental examples…