J. Moraga

most citedToric models of smooth Fano threefolds

1 citations · 1 across the 14 of their papers we have counts for

collaborators

15 papers

math.AG2025

Hyperbolicity of adjoint linear series on varieties with positive tangent bundle

Atsushi Ito, Joaquín Moraga, Debaditya Raychaudhury +1

Let $X$ be a smooth projective variety of dimension $n \geq 3$ , and let $L$ be an ample line bundle on $X$ . In this article, we study the algebraic hyperbolicity of a very general s…

math.AG2025

Fano compactifications of mutation algebras

Joshua Enwright, Luca Francone, Joaquín Moraga +1

In this article, we introduce the notion of mutation semigroup algebras. This concept simultaneously generalizes cluster algebras and semigroup algebras. We show that, under some m…

math.AG2025

Characterization of products of projective spaces via nef complexity

Joshua Enwright, Stefano Filipazzi, Yoshinori Gongyo +4

We define the nef complexity of a projective variety $X$ . This invariant compares $dim X + ρ (X)$ with the sum of the coefficients of nef partitions of $- K_{X}$ . We prove that the nef…

math.AG2025

Degenerations of cluster type varieties

Joaquín Moraga, Juan Pablo Zúñiga

We study degenerations of cluster type varieties and pairs. Our first theorem proves that degenerations of toric pairs are finite quotients of toric pairs. In a similar vein, under…

math.AG2025

Bott-Chern complexity of Kähler pairs

Christopher Hacon, Joaquín Moraga, José Ignacio Yáñez

We introduce the Bott-Chern complexity of a compact Kähler pair $(X, B)$ . This invariant compares $dim (X)$ , $dim H_{BC}^{1, 1} (X)$ and the sum of the coefficients of $B$ . When…

math.AG2024

Calabi-Yau pairs of complexity two

Joaquín Moraga, José Ignacio Yáñez

A Calabi-Yau pair of index one and complexity zero is toric. Furthermore, a Calabi-Yau pair of index one and complexity one is of cluster type. In this article, we study Calabi-Yau…

math.AG2024

A hyperbolicity conjecture for adjoint bundles

Joaquín Moraga, Wern Yeong

Let $X$ be a $n$ -dimensional smooth projective variety and $L$ be an ample Cartier divisor on $X$ . We conjecture that a very general element of the linear system $∣ K_{X} + (3 n + 1) L ∣$ is…

math.AG2024

Algebraic tori in the complement of quartic surfaces

Eduardo Alves da Silva, Fernando Figueroa, Joaquín Moraga

Let $B \subset P^{3}$ be an slc quartic surface. The existence of an embedding $G_{m}^{3} ↪ P^{3} ∖ B$ implies that $B$ has coregularity zero.…

math.AG2024

Toricity in families of Fano varieties

Lena Ji, Joaquín Moraga

Rationality is not a constructible property in families. In this article, we consider stronger notions of rationality and study their behavior in families of Fano varieties. We fir…

math.AG2024★ 1 cited

Toric models of smooth Fano threefolds

Konstantin Loginov, Joaquín Moraga, Artem Vasilkov

We prove that a general rational smooth Fano threefold admits a toric model. More precisely, for a general rational smooth Fano threefold $X$ , we show the existence of a boundary d…

math.AG2024

Polarized endomorphisms of log Calabi-Yau pairs

Joaquín Moraga, José Ignacio Yáñez, Wern Yeong

Let $(X, Δ)$ be a dlt log Calabi-Yau pair admitting a polarized endomorphism. We show that $(X, Δ)$ is a finite quotient of a toric log Calabi-Yau fibration over an abelian variety.…

math.AG2024

Birational complexity of log Calabi-Yau 3-folds

Joaquín Moraga

We study the birational complexity of log Calabi-Yau $3$ -folds. For such a pair $(X, B)$ of index one and coregularity zero, we show that $c_{bir} (X, B) \in {0, 2, 3}$ . Further, w…

math.AG2024

Log Calabi-Yau pairs of birational complexity zero

Joshua Enwright, Fernando Figueroa, Joaquín Moraga

In this article, we study the geometry of log Calabi-Yau pairs $(X, B)$ of index one and birational complexity zero. Firstly, we propose a conjecture that characterizes such pairs $…

math.AG2024

Birational complexity and conic fibrations

Joaquín Moraga

Let $(X, B)$ be a log Calabi-Yau pair of dimension $n$ , index one, and birational complexity $c$ . We show that $(X, B)$ has a crepant birational model that admits a tower of Mori fib…

math.AG2024

Birational complexity and dual complexes

Mirko Mauri, Joaquín Moraga

We introduce the notion of birational complexity of a log Calabi-Yau pair. This invariant measures how far the log Calabi-Yau pair is to being birational to a toric pair. We study…