9 citations · 31 across the 19 of their papers we have counts for
21 papers
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…
Enumeration of max-pooling responses with generalized permutohedra
Laura Escobar, Patricio Gallardo, Javier González-Anaya +3
We investigate the combinatorics of max-pooling layers, which are functions that downsample input arrays by taking the maximum over shifted windows of input coordinates, and which…
Unimodal singularities and boundary divisors in the KSBA moduli of a class of Horikawa surfaces
Patricio Gallardo, Gregory Pearlstein, Luca Schaffler +1
Smooth minimal surfaces of general type with , , and constitute a fundamental example in the geography of algebraic surfaces, and the 28-dimensional moduli spac…
Variation of stability for moduli spaces of unordered points in the plane
Patricio Gallardo, Benjamin Schmidt
We study compactifications of the moduli space of unordered points in the plane via variation of GIT quotients of their corresponding Hilbert scheme. Our VGIT considers linearizati…
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.
Quivers and moduli of their thin sincere representations in Macaulay2
Mary Barker, Patricio Gallardo
We introduce the Macaulay2 package ThinSincereQuivers for studying acyclic quivers, the moduli of their thin-sincere representations, and the reflexive flow polytopes associated to…
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…
Compactifications of the moduli space of plane quartics and two lines
Patricio Gallardo, Jesus Martinez-Garcia, Zheng Zhang
We study the moduli space of triples consisting of quartic curves and lines and . Specifically, we construct and compactify the moduli space in two w…
Families of elliptic curves in and Bridgeland Stability
Patricio Gallardo, César Lozano Huerta, Benjamin Schmidt
We study wall crossings in Bridgeland stability for the Hilbert scheme of elliptic quartic curves in three dimensional projective space. We provide a geometric description of each…
Moduli of cubic surfaces and their anticanonical divisors
Patricio Gallardo, Jesus Martinez-Garcia
We consider the moduli space of log smooth pairs formed by a cubic surface and an anticanonical divisor. We describe all compactifications of this moduli space which are constructe…
Wonderful compactifications of the moduli space of points in affine and projective space
Patricio Gallardo, Evangelos Routis
We introduce and study smooth compactifications of the moduli space of n labeled points with weights in projective space, which have normal crossings boundary and are defined as GI…
A Generic Slice of the Moduli Space of Line Arrangements
Kenneth Ascher, Patricio Gallardo
We study the compactification of the locus parametrizing lines with a fixed intersection to a given line, inside the moduli space of line arrangements in the projective plane const…
Variations of geometric invariant quotients for pairs, a computational approach
Patricio Gallardo, Jesus Martinez-Garcia
We study the GIT compactifications of pairs formed by a hypersurface and a hyperplane. We provide a general setting to characterize all polarizations which give rise to different G…
Modular interpretation of a non-reductive Chow quotient
Patricio Gallardo, Noah Giansiracusa
The space of n distinct points and a disjoint parameterized hyperplane in projective d-space up to projectivity---equivalently, configurations of n distinct points in affine d-spac…
A note on graded hypersurface singularities
Patricio Gallardo
For a weighted quasihomogeneous two dimensional hypersurface singularity, we define a smoothing with unipotent monodromy and an isolated graded normal singularity. We study the nat…
On the GIT Quotient Space of Quintic Surfaces
Patricio Gallardo
We describe the GIT compactification for the moduli space of smooth quintic surfaces in projective space. In particular, we show that a normal quintic surface with at worst an isol…