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arXiv · 2310.02844

The heart fan of an abelian category

Nathan Broomhead·David Pauksztello·David Ploog·Jon Woolf
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Abstract

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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BibTeXRIS

Nathan Broomhead, David Pauksztello, David Ploog, Jon Woolf. 2023-10-04. The heart fan of an abelian category. https://arxiv.org/abs/2310.02844

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