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Disconnectedness of stability manifolds and their geometric loci, and separation of braid orbits of semiorthogonal decompositions

  • Genki Ouchi
  • Tomoki Yoshida
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Abstract

This paper proves that the Bridgeland stability manifold Stab(X) has infinitely many connected components for general quintic threefolds, other general complete intersection Calabi--Yau threefolds, certain odd-dimensional Calabi--Yau varieties, and certain rational weak Fano varieties. Moreover, we show that the geometric locus Stabgeo(X) meets distinct connected components of Stab(X) for general quintic threefolds and their products with varieties with finite Albanese morphisms, which gives examples in any dimension at least three. For the weak Fano examples, we also construct semiorthogonal decompositions in infinitely many braid group orbits. The proof is an extension of Nordskova's argument to families, using semilinear autoequivalences and absolute Galois actions on geometric generic fibers to permute mutually orthogonal spherical objects. Then, we specialize the separation to closed fibers. In our examples, the spherical objects are constructed from rigid rational curves or spinor bundles on quadrics.

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Cite

BibTeXRIS
BibTeX
@misc{ouchi2026disconnectedness,
  title = {{Disconnectedness of stability manifolds and their geometric loci, and separation of braid orbits of semiorthogonal decompositions}},
  author = {Genki Ouchi and Tomoki Yoshida},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41344},
  eprint = {2610.41344},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41344},
}
RIS
TY  - UNPB
TI  - Disconnectedness of stability manifolds and their geometric loci, and separation of braid orbits of semiorthogonal decompositions
AU  - Genki Ouchi
AU  - Tomoki Yoshida
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41344
UR  - https://arxiv.org/abs/2610.41344
AB  - This paper proves that the Bridgeland stability manifold Stab(X) has infinitely many connected components for general quintic threefolds, other general complete intersection Calabi--Yau threefolds, certain odd-dimensional Calabi--Yau varieties, and certain rational weak Fano varieties. Moreover, we show that the geometric locus Stab^geo(X) meets distinct connected components of Stab(X) for general quintic threefolds and their products with varieties with finite Albanese morphisms, which gives examples in any dimension at least three. For the weak Fano examples, we also construct semiorthogonal decompositions in infinitely many braid group orbits. The proof is an extension of Nordskova's argument to families, using semilinear autoequivalences and absolute Galois actions on geometric generic fibers to permute mutually orthogonal spherical objects. Then, we specialize the separation to closed fibers. In our examples, the spherical objects are constructed from rigid rational curves or spinor bundles on quadrics.
ER  -