Establishes a correspondence between facet mutation classes of Fano simplices and positive integer solutions to associated weighted Markov-type equations, with mutations intertwined and applications to volume and multiplicity formulas.
Polygonal Quivers
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abstract
We show that Fano lattice polygons define a class of balanced quivers with interesting properties. The combinatorics of these quivers is related to singularities of the underlying toric Fano surface. This allows us to show that every Fano polygon defines a point on a certain family of algebraic hypersurfaces. Our quivers admit a generalized mutation which preserves balancing and coincides with combinatorial mutation of Fano polygons whenever both operations are defined. We characterize balanced quivers arising from Fano polygons and discuss generalizations to higher dimensions.
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math.AG 1years
2026 1verdicts
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Mutation of Fano Simplices and Markov type equations
Establishes a correspondence between facet mutation classes of Fano simplices and positive integer solutions to associated weighted Markov-type equations, with mutations intertwined and applications to volume and multiplicity formulas.