Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 7 min ago
PreprintarXiv licencearXiv

Generalized Iskovskikh surfaces and unirationality of del Pezzo surfaces of degree $2$

  • Runxuan Gao
Open at sourcePDFDOICite

Abstract

We introduce generalized Iskovskikh surfaces and study their relation to quasi-étale double covers. As an application, we prove that a del Pezzo surface of degree $2$ over an infinite field of characteristic different from $2$ is unirational if it has a rational generalized Eckardt point. This resolves a previously open case not covered by Manin's construction.

Related

  1. Closed points on del Pezzo surfaces of degree 4 and index 2
    Jean-Louis Colliot-Thélène, Federico Scavia
    HALPreprintCC BY 4.0Full textAlgebra & number theoryHAL
  2. Classification of low degree del Pezzo orbifolds II
    Saptarshi Dandapat
    arXivPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryarXiv
  3. Zero-cycles on del Pezzo surfaces : erratum and additions
    Jean-Louis Colliot-Thélène
    HALPreprintCC BY-NC-ND 4.0Full textGeneral mathematicsHAL
  4. Universal torsors over quartic del Pezzo surfaces and stable rationality
    Yuri Tschinkel, Zhijia Zhang
    arXivPreprintCC BY 4.0Full text1 citedAlgebra & number theoryarXiv
  5. Boundedness of geometrically integral ε-klt del Pezzo surfaces
    Shikha Bhutani, Sudipta Das
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{gao2026generalized,
  title = {{Generalized Iskovskikh surfaces and unirationality of del Pezzo surfaces of degree $2$}},
  author = {Runxuan Gao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39284},
  eprint = {2610.39284},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39284},
}
RIS
TY  - UNPB
TI  - Generalized Iskovskikh surfaces and unirationality of del Pezzo surfaces of degree $2$
AU  - Runxuan Gao
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39284
UR  - https://arxiv.org/abs/2610.39284
AB  - We introduce generalized Iskovskikh surfaces and study their relation to quasi-étale double covers. As an application, we prove that a del Pezzo surface of degree $2$ over an infinite field of characteristic different from $2$ is unirational if it has a rational generalized Eckardt point. This resolves a previously open case not covered by Manin's construction.
ER  -