Criterion for the accumulation of v-walls
dc.contributor.advisor
Maciocia, Antony
dc.contributor.advisor
Pridham, Jon
dc.contributor.author
Naylor, Luke
dc.contributor.sponsor
Engineering and Physical Sciences Research Council (EPSRC)
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dc.date.accessioned
2025-06-12T10:23:02Z
dc.date.available
2025-06-12T10:23:02Z
dc.date.issued
2025-06-12
dc.description.abstract
In this thesis we consider walls in the slice of geometric stability conditions for Chern characters on a principally abelian polarised surface. It is known that there is a vertical line of stability conditions in our choice of parametrisation, determined entirely numerically, which must intersect every wall, apart from a single vertical one. Furthermore if this line has rational horizontal coordinate β_ , then there can only be finitely many walls. In principal, when this horizontal coordinate is not rational, then there could be infinitely many walls. This has also been shown for certain examples and classes of Chern characters, but not exhaustively for all Chern characters where the aforementioned vertical line of stability conditions has irrational horizontal coordinate.
The main conclusion of this thesis is that all other classes of Chern characters not considered also have infinitely many walls. That is, a Chern character v on a principally polarised abelian surface 𝕋 with NS(𝕋) = ℤℓ has finitely many walls if and only if β_(v) is rational. The other aspect of this thesis is developing methods to computing possibilities for walls more efficiently.
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dc.identifier.uri
https://hdl.handle.net/1842/43553
dc.identifier.uri
http://dx.doi.org/10.7488/era/6087
dc.language.iso
en
en
dc.publisher
The University of Edinburgh
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dc.relation.hasversion
Luke Naylor. Lnay/Pseudo_tilt_py. May 24, 2023. url: https://github.com/ lnay/pseudo_tilt_py (visited on 05/11/2024).
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dc.relation.hasversion
Luke Naylor. Pseudo-Wall Finder, Try by Scanning QR Code at Top-Right. GitLab, 2023. url: https://gitlab.com/pseudowalls/tilt.rs.
en
dc.relation.hasversion
Luke Naylor. Lnay/Tilt-Rs-Notebook. Jan. 23, 2024. url: https : / / github . com/lnay/tilt-rs-notebook (visited on 05/11/2024).
en
dc.relation.hasversion
Luke Naylor. Pseudo_tilt - Rust. July 18, 2024. url: https://pseudowalls. gitlab.io/tilt.rs/pseudo_tilt/ (visited on 07/18/2024).
en
dc.relation.hasversion
Luke Naylor. Pseudowalls Page on Luke Naylor’s Site. 2024. url: https : / / lukideangeometry.xyz/pseudowalls (visited on 05/11/2024).
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dc.subject
Bridgeland stability conditions
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dc.subject
walls
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dc.subject
algebraic geometry
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dc.title
Criterion for the accumulation of v-walls
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dc.type
Thesis or Dissertation
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dc.type.qualificationlevel
Doctoral
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dc.type.qualificationname
PhD Doctor of Philosophy
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