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The Global Dimension Function on Stability Manifolds

  • Dongjian Wu
  • Nantao Zhang
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Abstract

In this paper, we study the reachability and boundary behavior of the global dimension function on Bridgeland stability manifolds. For a smooth projective variety X of dimension n, we prove that the infimum of the global dimension function is n. This value is attained when −KX is ample, is taken by every stability condition when KX∈Pic0(X), and is not attained when KX is big and nef. We also extend these reachability results to pre-stability conditions. In addition, we construct compactifications of reduced stability spaces of smooth projective curves to which the global dimension function extends continuously. Finally, we discuss algebraic models of the reachability problem, including finite-dimensional algebras and semiorthogonal decompositions.

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Cite

BibTeXRIS
BibTeX
@misc{wu2026global,
  title = {{The Global Dimension Function on Stability Manifolds}},
  author = {Dongjian Wu and Nantao Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.28187},
  eprint = {2608.28187},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.28187},
}
RIS
TY  - UNPB
TI  - The Global Dimension Function on Stability Manifolds
AU  - Dongjian Wu
AU  - Nantao Zhang
PY  - 2026
DA  - 2026/08/28
PB  - arXiv
DO  - 10.48550/arxiv.2608.28187
UR  - https://arxiv.org/abs/2608.28187
AB  - In this paper, we study the reachability and boundary behavior of the global dimension function on Bridgeland stability manifolds. For a smooth projective variety X of dimension n, we prove that the infimum of the global dimension function is n. This value is attained when −K_X is ample, is taken by every stability condition when K_X∈Pic^0(X), and is not attained when K_X is big and nef. We also extend these reachability results to pre-stability conditions. In addition, we construct compactifications of reduced stability spaces of smooth projective curves to which the global dimension function extends continuously. Finally, we discuss algebraic models of the reachability problem, including finite-dimensional algebras and semiorthogonal decompositions.
ER  -