Fourier-Mukai Transforms and Stable Sheaves on Weierstrass Elliptic Surfaces
On a Weierstraß elliptic surface X, we define a “limit” of Bridgeland stability conditions, denoted as-stability, by moving the polarisation towards the fiber direction in the ample cone while keeping the volume of the polarisation fixed. We describe conditions under which a slope stable torsion-fre...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2024
- Institución:
- Universidad del Rosario
- Repositorio:
- Repositorio EdocUR - U. Rosario
- Idioma:
- eng
- OAI Identifier:
- oai:repository.urosario.edu.co:10336/44806
- Acceso en línea:
- https://doi.org/10.1007/s00574-024-00422-7
https://repository.urosario.edu.co/handle/10336/44806
- Palabra clave:
- Weierstrass surface
Elliptic surface
Fourier-Mukai transform
Stability
- Rights
- License
- Attribution-NonCommercial-NoDerivatives 4.0 International
| Summary: | On a Weierstraß elliptic surface X, we define a “limit” of Bridgeland stability conditions, denoted as-stability, by moving the polarisation towards the fiber direction in the ample cone while keeping the volume of the polarisation fixed. We describe conditions under which a slope stable torsion-free sheaf is taken by a Fourier-Mukai transform to a -stable object, and describe a modification upon which a-semistable object is taken by the inverse Fourier-Mukai transform to a slope semistable torsion-free sheaf. We also study wall-crossing for Bridgeland stability, and show that 1-dimensional twisted Gieseker semistable sheaves are taken by a Fourier-Mukai transform to Bridgeland semistable objects. |
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