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math.AG2026

Valuative independence and cluster theta reciprocity

Man-Wai Cheung, Timothy Magee, Travis Mandel +1

We prove that theta functions constructed from positive scattering diagrams satisfy valuative independence. That is, for certain valuations , we have $\oper…

math.AG2026

Fundamentals of Broken Line Convex Geometry

Juan Bosco Frías-Medina, Timothy Magee

We develop the fundamentals of a new theory of convex geometry -- which we call "broken line convex geometry". This is a theory of convexity where the ambient space is the rational…

math.AG2024

Newton--Okounkov bodies and minimal models for cluster varieties

Lara Bossinger, Man-Wai Cheung, Timothy Magee +1

Let be a (partial) minimal model of a scheme with a cluster structure. Under natural assumptions, for every choice of seed we associate a Newton--Okounkov body to every div…

math.AG2024

Toric degenerations of cluster varieties and cluster duality

Lara Bossinger, Bosco Frías-Medina, Timothy Magee +1

We introduce the notion of a -pattern with coefficients and its geometric counterpart: a cluster -variety with coefficients. We use these constructions to build a f…