9 citations · 43 across the 18 of their papers we have counts for
19 papers · 1 filter
The CompGIT package: a computational tool for Geometric Invariant Theory quotients
Robert Hanson, Jesus Martinez-Garcia
We describe CompGIT, a SageMath package to describe Geometric Invariant Theory (GIT) quotients of projective space by simple groups. The implementation is based on algorithms descr…
Two remarks on asymptotically log Fano pairs
Jesus Martinez-Garcia
Asymptotically log Fano pairs were introduced by Cheltsov and Rubinstein, generalising a definition of Maeda. They have received attention in the last decade within the theory of K…
K-moduli of log del Pezzo pairs and variations of GIT
Jesus Martinez-Garcia, Theodoros Stylianos Papazachariou, Junyan Zhao
We study the K-moduli of log del Pezzo pairs formed by a del Pezzo surface of degree and an anti-canonical divisor. These moduli spaces naturally depend on one parameter, provi…
K-stability of Casagrande-Druel varieties
Ivan Cheltsov, Tiago Duarte Guerreiro, Kento Fujita +2
We introduce a new subclass of Fano varieties (Casagrande-Druel varieties), that are -dimensional varieties constructed from Fano double covers of dimension . We conjecture…
One-dimensional components in the K-moduli of smooth Fano 3-folds
Hamid Abban, Ivan Cheltsov, Elena Denisova +5
By identifying K-polystable limits in 4 specific deformations families of smooth Fano 3-folds, we complete the classification of one-dimensional components in the K-moduli space of…
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…
On maximally non-factorial nodal Fano threefolds
Ivan Cheltsov, Igor Krylov, Jesus Martinez-Garcia +1
We classify non-factorial nodal Fano threefolds with node and class group of rank .
Some observations on the dimension of Fano K-moduli
Jesus Martinez-Garcia, Cristiano Spotti
In this short note we show the unboundedness of the dimension of the K-moduli space of -dimensional Fano varieties, and that the dimension of the stack can also be unbounded whi…
On the body of ample angles of asymptotically log Fano varieties
Paolo Cascini, Jesus Martinez-Garcia, Yanir A. Rubinstein
In dimension two, we reduce the classification problem for asymptotically log Fano pairs to the problem of determining generality conditions on certain blow-ups. In any dimension,…
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…
Constant scalar curvature Kähler metrics on rational surfaces
Jesus Martinez-Garcia
We consider projective rational strong Calabi dream surfaces: projective smooth rational surfaces which admit a constant scalar curvature Kähler metric for every Kähler class. We s…
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…
Unstable polarized del Pezzo surfaces
Ivan Cheltsov, Jesus Martinez-Garcia
We provide new examples of K-unstable polarized smooth del Pezzo surfaces using a flopped version first used by Cheltsov and Rubinstein of the test configurations introduced by Ros…
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…
Stable polarized del Pezzo surfaces
Ivan Cheltsov, Jesus Martinez-Garcia
We give a simple sufficient condition for K-stability of polarized del Pezzo surfaces and for the existence of a constant scalar curvature Kahler metric in the Kahler class corresp…
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…
Dynamic alpha-invariants of del Pezzo surfaces
Ivan Cheltsov, Jesus Martinez-Garcia
For every smooth del Pezzo surface , smooth curve and , we compute the -invariant of Tian and prove the existence of Kähler--Einstein…
Dynamic alpha-invariants of del Pezzo surfaces with boundary
Jesus Martinez-Garcia
The global log canonical threshold (or Tian's alpha-invariant) plays an important role in the geometry of Fano varieties. Tian showed that Fano manifolds with big alpha-invariant c…
Log canonical thresholds of Del Pezzo Surfaces in characteristic p
Jesus Martinez-Garcia
The global log canonical threshold of each non-singular complex del Pezzo surface was computed by Cheltsov. The proof used Kollár-Shokurov's connectedness principle and other resul…