On Degenerations of the Projective Plane
Complementing the results of Hacking and Prokhorov, we determine explicitly all log-terminal, rational, degenerations of the projective plane that admit a non-trivial torus action.
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2025 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2025
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/213535 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On Degenerations of the Projective Plane. Jürgen Hausen, Katharina Király and Milena Wrobel. SIGMA 21 (2025), 042, 16 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862746044140355584 |
|---|---|
| author | Hausen, Jürgen Király, Katharina Wrobel, Milena |
| author_facet | Hausen, Jürgen Király, Katharina Wrobel, Milena |
| citation_txt | On Degenerations of the Projective Plane. Jürgen Hausen, Katharina Király and Milena Wrobel. SIGMA 21 (2025), 042, 16 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Complementing the results of Hacking and Prokhorov, we determine explicitly all log-terminal, rational, degenerations of the projective plane that admit a non-trivial torus action.
|
| first_indexed | 2026-03-21T18:50:24Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-213535 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T18:50:24Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Hausen, Jürgen Király, Katharina Wrobel, Milena 2026-02-18T11:27:44Z 2025 On Degenerations of the Projective Plane. Jürgen Hausen, Katharina Király and Milena Wrobel. SIGMA 21 (2025), 042, 16 pages 1815-0659 2020 Mathematics Subject Classification: 14L30; 14J26; 14J10; 14D06 arXiv:2405.04862 https://nasplib.isofts.kiev.ua/handle/123456789/213535 https://doi.org/10.3842/SIGMA.2025.042 Complementing the results of Hacking and Prokhorov, we determine explicitly all log-terminal, rational, degenerations of the projective plane that admit a non-trivial torus action. We would like to thank Yuchen Liu for the fruitful discussions that stimulated this work. Moreover, we are grateful to Andrea Petracci for valuable information about existing articles on algebraic geometry around the Markov numbers. Finally, we are indebted to the referees for carefully going through our manuscript, for valuable suggestions, and for pointing out a gap in the proof of a former, incorrect version of the second main theorem. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Degenerations of the Projective Plane Article published earlier |
| spellingShingle | On Degenerations of the Projective Plane Hausen, Jürgen Király, Katharina Wrobel, Milena |
| title | On Degenerations of the Projective Plane |
| title_full | On Degenerations of the Projective Plane |
| title_fullStr | On Degenerations of the Projective Plane |
| title_full_unstemmed | On Degenerations of the Projective Plane |
| title_short | On Degenerations of the Projective Plane |
| title_sort | on degenerations of the projective plane |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/213535 |
| work_keys_str_mv | AT hausenjurgen ondegenerationsoftheprojectiveplane AT kiralykatharina ondegenerationsoftheprojectiveplane AT wrobelmilena ondegenerationsoftheprojectiveplane |