Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 10 min ago
Peer-reviewedCC BYGeometry & Topology

Stability conditions on products of curves and Hilbert schemes of surfaces

  • Chunyi Li1
  • Emanuele Macrì2
  • Alexander Perry3
  • Paolo Stellari4
  • Xiaolei Zhao5
5 affiliations
  1. 1Mathematical Institute, University of Warwick, Coventry, United Kingdom
  2. 2Laboratoire de Mathématiques d’Orsay, Université Paris-Saclay, Orsay, France
  3. 3Department of Mathematics, University of Michigan, Ann Arbor, MI, United States
  4. 4Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Milan, Italy
  5. 5Department of Mathematics, University of California, Santa Barbara, Santa Barbara, CA, United States
Open at sourcePDFDOICite

Abstract

We prove that stability conditions on the derived category of a product of curves of positive genus are uniquely determined by their central charge and the phase of skyscraper sheaves.As an application, we construct stability conditions on Hilbert schemes of points on certain surfaces, including some K3 surfaces of Kummer type.

Related

  1. Hochschild cohomology of Hilbert schemes of points on surfaces
    Pieter Belmans, Lie Fu, Andreas Krug
    Journal für die reine und angewandte MathematikPeer-reviewedCC BY 4.0Full textGeometry & topologyHAL
  2. Nef cone decompositions for nested Hilbert schemes of points on surfaces
    Chiwon Yoon
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. Degenerate complex structures on surfaces and stability conditions
    Antonios-Alexandros Robotis, Nicolás Vilches
    arXivPreprintarXiv licenceFull textAlgebra & number theoryGeometry & topologyarXiv
  4. A note on stability conditions on product-quotient surfaces
    Uttaran Dutta
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. Non-reducedness of the Hilbert schemes of few points
    Michał Szachniewicz
    Mathematische ZeitschriftPeer-reviewedLicence not statedFull text15 citedGeometry & topologyOpenAlex

Cite

BibTeXRIS
BibTeX
@article{li2026stability,
  title = {{Stability conditions on products of curves and Hilbert schemes of surfaces}},
  author = {Chunyi Li and Emanuele Macrì and Alexander Perry and Paolo Stellari and Xiaolei Zhao},
  journal = {Geometry \& Topology},
  year = {2026},
  month = oct,
  doi = {10.2140/gt.2026.30.3485},
  url = {https://doi.org/10.2140/gt.2026.30.3485},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Stability conditions on products of curves and Hilbert schemes of surfaces
AU  - Chunyi Li
AU  - Emanuele Macrì
AU  - Alexander Perry
AU  - Paolo Stellari
AU  - Xiaolei Zhao
PY  - 2026
DA  - 2026/10/12
JO  - Geometry & Topology
DO  - 10.2140/gt.2026.30.3485
UR  - https://doi.org/10.2140/gt.2026.30.3485
AB  - We prove that stability conditions on the derived category of a product of curves of positive genus are uniquely determined by their central charge and the phase of skyscraper sheaves.As an application, we construct stability conditions on Hilbert schemes of points on certain surfaces, including some K3 surfaces of Kummer type.
SN  - 1364-0380
SN  - 1465-3060
ER  -