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The heart fan of an abelian category

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arxiv 2310.02844 v2 pith:2ANZCQ7R submitted 2023-10-04 math.RT math.AG

Nathan Broomhead , David Pauksztello , David Ploog , Jon Woolf This is my paper · ORCID
classification math.RTmath.AG
keywords heartabeliancategoryconesalgebraapplyboundedbridgeland
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We apply convex geometry (cones, fans) to homological input (abelian categories, hearts of bounded t-structures) to construct a new invariant of an abelian category, its heart fan. This can be viewed as a `universal phase diagram' for Bridgeland stability conditions with the given heart. When the abelian category is the module category of a finite-dimensional algebra, the heart fan is complete and contains the g-fan as the subfan of full-dimensional cones. The heart fan is also closely related to the wall-and-chamber structure for King semistability.

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  1. Wide subcategories and brick-finiteness for length categories

    math.RT 2026-07 conditional novelty 6.0 of 10

    A finite-rank abelian length category is brick-finite if and only if it is widely determined and widely co-determined.

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