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: Hausen, Jürgen, Király, Katharina, Wrobel, Milena
Format: Article
Language:English
Published: Інститут математики НАН України 2025
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
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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
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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
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AT kiralykatharina ondegenerationsoftheprojectiveplane
AT wrobelmilena ondegenerationsoftheprojectiveplane