15 citations · 77 across the 33 of their papers we have counts for
41 papers
Cluster type varieties
Joaquín Moraga
Cluster type varieties are compactifications of algebraic tori on which the volume form has no zeros. These form a natural class of varieties that generalizes both toric varieties…
The geometric cone conjecture in relative dimension two
Joaquín Moraga, Talon Stark
Let be a fibration of relative dimension at most two and let be a klt pair for which . We show that there are only finitely many Mori cham…
Polarized endomorphisms of Fano varieties with complements
Joaquín Moraga, José Ignacio Yáñez, Wern Yeong
Let be a Fano type variety and be a log Calabi-Yau pair with a Weil divisor. If admits a polarized endomorphism, then we show that is a finite quoti…
Fundamental groups of log Calabi-Yau surfaces
Cécile Gachet, Zhining Liu, Joaquín Moraga
In this article, we study the orbifold fundamental group of a Calabi--Yau pair with log canonical singularities. We conjecture that the orbifold fundam…
Symmetries of Fano varieties
Louis Esser, Lena Ji, Joaquín Moraga
We study Fano varieties endowed with a faithful action of a symmetric group, as well as analogous results for Calabi--Yau varieties, and log terminal singularities. We show the exi…
Fundamental groups of low-dimensional lc singularities
Fernando Figueroa, Joaquín Moraga
In this article, we study the fundamental groups of low-dimensional log canonical singularities, i.e., log canonical singularities of dimension at most . In dimension , we sh…
Generalized complexity of surfaces
Yoshinori Gongyo, Joaquín Moraga
In this article, we introduce the generalized complexity of a generalized Calabi--Yau pair . This invariant compares the dimension of and Picard rank of w…
Complements and coregularity of Fano varieties
Fernando Figueroa, Stefano Filipazzi, Joaquín Moraga +1
We study the relation between the coregularity, the index of log Calabi-Yau pairs, and the complements of Fano varieties. We show that the index of a log Calabi-Yau pair of…
Reductive covers of klt varieties
Lukas Braun, Joaquín Moraga
In this article, we study -covers of klt varieties, where is a reductive group. First, we exhibit an example of a klt singularity admitting a $\mathbb{P}{\rm GL}_n(\mathbb{K…
Index of coregularity zero log Calabi-Yau pairs
Stefano Filipazzi, Mirko Mauri, Joaquín Moraga
In this article, we study the index of log Calabi--Yau pairs of coregularity 0. We show that , where is the Weil index of . This is in contrast…
Coregularity of Fano varieties
Joaquín Moraga
The regularity of a Fano variety, denoted by , is the largest dimension of the dual complex of a log Calabi--Yau structure on . The coregularity is defined to be \…
On the boundedness of singularities via normalized volume
Yuchen Liu, Joaquín Moraga, Hendrik Süß
In this article we study conjectures regarding normalized volume and boundedness of singularities. We focus on singularities with a torus action of complexity 1, threefold singular…
Log canonical thresholds and coregularity
Fernando Figueroa, Joaquín Moraga, Junyao Peng
We prove the ascending chain condition for log canonical thresholds of bounded coregularity.
Bounding toric singularities with normalized volume
Joaquín Moraga, Hendrik Süß
We study the normalized volume of toric singularities. As it turns out, there is a close relation to the notion of (non-symmetric) Mahler volume from convex geometry. This observat…
Reductive quotients of klt singularities
Lukas Braun, Daniel Greb, Kevin Langlois +1
We prove that the quotient of a klt type singularity by a reductive group is of klt type. In particular, given a klt variety endowed with the action of a reductive group an…
Minimal log discrepancies of regularity one
Joaquín Moraga
In this article, we use the cone of nef curves to study minimal log discrepancies. The first result is an improvement of the nef cone theorem in the case of log Calabi-Yau dlt pair…
On termination of flips and fundamental groups
Joaquín Moraga
In this article, we propose a boundedness conjecture for the regional fundamental group of klt singularities. We prove that this boundedness conjecture, the Zariski closedness of t…
A geometric characterization of toric singularities
Joaquín Moraga, Roberto Svaldi
Given a projective contraction and a log canonical pair such that is nef over a neighborhood of a closed point , one can define…
On a toroidalization for klt singularities
Joaquín Moraga
In this article, we prove a toroidalization principle for finite actions on klt singularities. As an application, we prove that the Jordan property for the regional fundamental gro…
Iteration of Cox rings of klt singularities
Lukas Braun, Joaquín Moraga
Given a klt singularity , we define the iteration of Cox rings of . The first result of this article is that the iteration of Cox rings o…
Maximal log Fano manifolds are generalized Bott towers
Konstantin Loginov, Joaquín Moraga
We prove that maximal log Fano manifolds are generalized Bott towers. As an application, we prove that in each dimension, there is a unique maximal snc Fano variety satisfying Frie…
Small quotient minimal log discrepancies
Joaquín Moraga
We prove that for each positive integer there exists a positive number so that -dimensional toric quotient singularities satisfy the ACC for mld's on the interval $(0,…
Kawamata log terminal singularities of full rank
Joaquín Moraga
We study Kawamata log terminal singularities of full rank, i.e., -dimensional klt singularities containing a large finite abelian group of rank in its regional fundamental g…
Special termination for log canonical pairs
Vladimir Lazić, Joaquín Moraga, Nikolaos Tsakanikas
We prove the special termination for log canonical pairs and its generalisation in the context of generalised pairs.