Stability conditions supported on Lefschetz classes

Franco Giovenzana, Antonios-Alexandros Robotis, Franco Rota, Vanja Zuliani

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.

Disclosure

“ss, we feel that the present note is worth publishing since the techniques used are different than Cheng’s and provide an elementary proof of the full support property, albeit in a restricted class of examples. AI statement. Though we used Large Language Models for literature searches, all of the contents of this article were conceived of and written by the authors.”
PDF page 2

Classification: Literature search
Multiplier: 2
Verified: 2026-08-23T05:18:50.634444Z

Structural counts

Pages 13 pdf

Theorems 5 source

Lemmas 5 source

Propositions 5 source

Corollaries 3 source

Definitions 4 source

Displayed equations 35 source

Bibliography entries 0 source

Appendix pages 0 estimated

Count notes

Source counts use the expanded primary TeX file main.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.