Joaquín Moraga

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math.AG2026

Cluster type varieties

JoaquÃn 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…

math.AG2025

Termination of pseudo-effective 4-fold flips

JoaquÃn Moraga

Let $(X, I^)$ be a log canonical $4$ -fold over an algebraically closed field of characteristic zero. We prove that any sequence of $(K_{X} + I^)$ -flips terminates.

math.AG2025

Fundamental groups of log Calabi-Yau surfaces

CÃ©cile Gachet, Zhining Liu, JoaquÃn Moraga

In this article, we study the orbifold fundamental group $I ¨ _{1}^{orb} (X, I^)$ of a Calabi--Yau pair $(X, I^)$ with log canonical singularities. We conjecture that the orbifold fun…

math.AG2024

The geometric cone conjecture in relative dimension two

JoaquÃn Moraga, Talon Stark

Let $X \to S$ be a fibration of relative dimension at most two and let $(X, I^)$ be a klt pair for which $K_{X} + I^ \equiv_{S} 0$ . We show that there are only finitely many Mori ch…

math.AG2024

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 $X$ endowed with the action of a reductive group $G$ an…

math.AG2024

Complements and coregularity of Fano varieties

Fernando Figueroa, Stefano Filipazzi, JoaquÃn 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 $(X, B)$ of…