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Stability conditions supported on Lefschetz classes

  • Franco Giovenzana
  • Antonios-Alexandros Robotis
  • Franco Rota
  • Vanja Zuliani
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Abstract

Recently, C. Li constructed stability conditions on the derived categories of all smooth complex projective varieties. These stability conditions satisfy the support property of Kontsevich-Soibelman with respect to the lattice in cohomology generated by powers of an ample class. We extend Li's results to construct stability conditions with full support on Lefschetz type varieties whose algebraic cohomology is generated by divisor classes. This includes all smooth complex projective varieties of dimension at most 3 and smooth projective toric varieties.

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Cite

BibTeXRIS
BibTeX
@misc{giovenzana2026stability,
  title = {{Stability conditions supported on Lefschetz classes}},
  author = {Franco Giovenzana and Antonios-Alexandros Robotis and Franco Rota and Vanja Zuliani},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.16013},
  eprint = {2608.16013},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.16013},
}
RIS
TY  - UNPB
TI  - Stability conditions supported on Lefschetz classes
AU  - Franco Giovenzana
AU  - Antonios-Alexandros Robotis
AU  - Franco Rota
AU  - Vanja Zuliani
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2608.16013
UR  - https://arxiv.org/abs/2608.16013
AB  - Recently, C. Li constructed stability conditions on the derived categories of all smooth complex projective varieties. These stability conditions satisfy the support property of Kontsevich-Soibelman with respect to the lattice in cohomology generated by powers of an ample class. We extend Li's results to construct stability conditions with full support on Lefschetz type varieties whose algebraic cohomology is generated by divisor classes. This includes all smooth complex projective varieties of dimension at most 3 and smooth projective toric varieties.
ER  -