The heart fan of an abelian category
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
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| _version_ | 1866913491673153536 |
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| author | Broomhead, Nathan Pauksztello, David Ploog, David Woolf, Jon |
| author_facet | Broomhead, Nathan Pauksztello, David Ploog, David Woolf, Jon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_02844 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The heart fan of an abelian category Broomhead, Nathan Pauksztello, David Ploog, David Woolf, Jon Representation Theory Algebraic Geometry 18G80, 16E35, 14F08, 18E40, 52A20 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. |
| title | The heart fan of an abelian category |
| topic | Representation Theory Algebraic Geometry 18G80, 16E35, 14F08, 18E40, 52A20 |
| url | https://arxiv.org/abs/2310.02844 |