5 papers · 1 filter
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…
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 . This invariant compares with the sum of the coefficients of nef partitions of . We prove that the nef…
Complexity one varieties are cluster type
Joshua Enwright, Jennifer Li, José Ignacio Yáñez
The complexity of a Calabi-Yau pair is an invariant that relates the dimension of , the rank of the group of divisors, and the coefficients of . If the complexity is…
Log Calabi--Yau pairs of complexity zero and arbitrary index
Joshua Enwright, Fernando Figueroa
In this article, we give a characterization of log Calabi--Yau pairs of complexity zero and arbitrary index. As an application, we show that a log Calabi--Yau pair of birational co…
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 of index one and birational complexity zero. Firstly, we propose a conjecture that characterizes such pairs $…