Walls and asymptotics for Bridgeland stability conditions on 3-folds
We consider Bridgeland stability conditions for three-folds conjectured by Bayer-Macr\`i-Toda in the case of Picard rank one. We study the differential geometry of numerical walls, characterizing when they are bounded, discussing possible intersections, and showing that they are essentially regular....
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Association Epiga
2022-12-01
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| Series: | Épijournal de Géométrie Algébrique |
| Subjects: | |
| Online Access: | https://epiga.episciences.org/6819/pdf |
| _version_ | 1797248751661744128 |
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| author | Marcos Jardim Antony Maciocia |
| author_facet | Marcos Jardim Antony Maciocia |
| author_sort | Marcos Jardim |
| collection | DOAJ |
| description | We consider Bridgeland stability conditions for three-folds conjectured by
Bayer-Macr\`i-Toda in the case of Picard rank one. We study the differential
geometry of numerical walls, characterizing when they are bounded, discussing
possible intersections, and showing that they are essentially regular. Next, we
prove that walls within a certain region of the upper half plane that
parametrizes geometric stability conditions must always intersect the curve
given by the vanishing of the slope function and, for a fixed value of s, have
a maximum turning point there. We then use all of these facts to prove that
Gieseker semistability is equivalent to asymptotic semistability along a class
of paths in the upper half plane, and to show how to find large families of
walls. We illustrate how to compute all of the walls and describe the
Bridgeland moduli spaces for the Chern character (2,0,-1,0) on complex
projective 3-space in a suitable region of the upper half plane. |
| first_indexed | 2024-04-24T20:19:34Z |
| format | Article |
| id | doaj.art-750efe0dd3f0440c86fb42c33dd120de |
| institution | Directory Open Access Journal |
| issn | 2491-6765 |
| language | English |
| last_indexed | 2024-04-24T20:19:34Z |
| publishDate | 2022-12-01 |
| publisher | Association Epiga |
| record_format | Article |
| series | Épijournal de Géométrie Algébrique |
| spelling | doaj.art-750efe0dd3f0440c86fb42c33dd120de2024-03-22T09:11:16ZengAssociation EpigaÉpijournal de Géométrie Algébrique2491-67652022-12-01Volume 610.46298/epiga.2022.68196819Walls and asymptotics for Bridgeland stability conditions on 3-foldsMarcos JardimAntony MaciociaWe consider Bridgeland stability conditions for three-folds conjectured by Bayer-Macr\`i-Toda in the case of Picard rank one. We study the differential geometry of numerical walls, characterizing when they are bounded, discussing possible intersections, and showing that they are essentially regular. Next, we prove that walls within a certain region of the upper half plane that parametrizes geometric stability conditions must always intersect the curve given by the vanishing of the slope function and, for a fixed value of s, have a maximum turning point there. We then use all of these facts to prove that Gieseker semistability is equivalent to asymptotic semistability along a class of paths in the upper half plane, and to show how to find large families of walls. We illustrate how to compute all of the walls and describe the Bridgeland moduli spaces for the Chern character (2,0,-1,0) on complex projective 3-space in a suitable region of the upper half plane.https://epiga.episciences.org/6819/pdfmathematics - algebraic geometrymathematics - category theorymathematics - differential geometry14f08 (primary) 14a30, 14d20, 14j30, 18g80, 53a05 (secondary) |
| spellingShingle | Marcos Jardim Antony Maciocia Walls and asymptotics for Bridgeland stability conditions on 3-folds Épijournal de Géométrie Algébrique mathematics - algebraic geometry mathematics - category theory mathematics - differential geometry 14f08 (primary) 14a30, 14d20, 14j30, 18g80, 53a05 (secondary) |
| title | Walls and asymptotics for Bridgeland stability conditions on 3-folds |
| title_full | Walls and asymptotics for Bridgeland stability conditions on 3-folds |
| title_fullStr | Walls and asymptotics for Bridgeland stability conditions on 3-folds |
| title_full_unstemmed | Walls and asymptotics for Bridgeland stability conditions on 3-folds |
| title_short | Walls and asymptotics for Bridgeland stability conditions on 3-folds |
| title_sort | walls and asymptotics for bridgeland stability conditions on 3 folds |
| topic | mathematics - algebraic geometry mathematics - category theory mathematics - differential geometry 14f08 (primary) 14a30, 14d20, 14j30, 18g80, 53a05 (secondary) |
| url | https://epiga.episciences.org/6819/pdf |
| work_keys_str_mv | AT marcosjardim wallsandasymptoticsforbridgelandstabilityconditionson3folds AT antonymaciocia wallsandasymptoticsforbridgelandstabilityconditionson3folds |