Packing Densities of Delzant and Semitoric Polygons
Exploiting the relationship between 4-dimensional toric and semitoric integrable systems with Delzant and semitoric polygons, respectively, we develop techniques to compute certain equivariant packing densities and equivariant capacities of these systems by working exclusively with the polygons. Thi...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2023 |
| Автори: | , , , , , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2023
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212050 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Packing Densities of Delzant and Semitoric Polygons. Yu Du, Gabriel Kosmacher, Yichen Liu, Jeff Massman, Joseph Palmer, Timothy Thieme, Jerry Wu and Zheyu Zhang. SIGMA 19 (2023), 081, 42 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862696249088540672 |
|---|---|
| author | Du, Yu Kosmacher, Gabriel Liu, Yichen Massman, Jeff Palmer, Joseph Thieme, Timothy Wu, Jerry Zhang, Zheyu |
| author_facet | Du, Yu Kosmacher, Gabriel Liu, Yichen Massman, Jeff Palmer, Joseph Thieme, Timothy Wu, Jerry Zhang, Zheyu |
| citation_txt | Packing Densities of Delzant and Semitoric Polygons. Yu Du, Gabriel Kosmacher, Yichen Liu, Jeff Massman, Joseph Palmer, Timothy Thieme, Jerry Wu and Zheyu Zhang. SIGMA 19 (2023), 081, 42 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Exploiting the relationship between 4-dimensional toric and semitoric integrable systems with Delzant and semitoric polygons, respectively, we develop techniques to compute certain equivariant packing densities and equivariant capacities of these systems by working exclusively with the polygons. This expands on the results of Pelayo and Pelayo-Schmidt. We compute the densities of several important examples, and we also use our techniques to solve the equivariant semitoric perfect packing problem, i.e., we list all semitoric polygons for which the associated semitoric system admits an equivariant packing that fills all but a set of measure zero of the manifold. This paper also serves as a concise and accessible introduction to Delzant and semitoric polygons in dimension four.
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| first_indexed | 2026-03-18T06:51:35Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212050 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-18T06:51:35Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Du, Yu Kosmacher, Gabriel Liu, Yichen Massman, Jeff Palmer, Joseph Thieme, Timothy Wu, Jerry Zhang, Zheyu 2026-01-23T10:13:10Z 2023 Packing Densities of Delzant and Semitoric Polygons. Yu Du, Gabriel Kosmacher, Yichen Liu, Jeff Massman, Joseph Palmer, Timothy Thieme, Jerry Wu and Zheyu Zhang. SIGMA 19 (2023), 081, 42 pages 1815-0659 2020 Mathematics Subject Classification: 37J35; 53D20; 37J06 arXiv:2210.06415 https://nasplib.isofts.kiev.ua/handle/123456789/212050 https://doi.org/10.3842/SIGMA.2023.081 Exploiting the relationship between 4-dimensional toric and semitoric integrable systems with Delzant and semitoric polygons, respectively, we develop techniques to compute certain equivariant packing densities and equivariant capacities of these systems by working exclusively with the polygons. This expands on the results of Pelayo and Pelayo-Schmidt. We compute the densities of several important examples, and we also use our techniques to solve the equivariant semitoric perfect packing problem, i.e., we list all semitoric polygons for which the associated semitoric system admits an equivariant packing that fills all but a set of measure zero of the manifold. This paper also serves as a concise and accessible introduction to Delzant and semitoric polygons in dimension four. This paper is the result of three semesters of work supported by the Illinois Geometry Lab (IGL) program at the University of Illinois at Urbana-Champaign. We are very thankful to the IGL for their support. We are also thankful to Parth Deshmukh, Felipe Pallo Rivadeneira, Haoxiang Sun, Deming Tian, and Tongshu Liu for their hard work in earlier IGL projects tangentially related to this one. We also thank Marino Romero for encouraging us to compile our results into this paper, and Yohann Le Floch for many helpful comments and suggestions on an early version. Finally, we also thank the referees who gave very helpful comments, which improved the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Packing Densities of Delzant and Semitoric Polygons Article published earlier |
| spellingShingle | Packing Densities of Delzant and Semitoric Polygons Du, Yu Kosmacher, Gabriel Liu, Yichen Massman, Jeff Palmer, Joseph Thieme, Timothy Wu, Jerry Zhang, Zheyu |
| title | Packing Densities of Delzant and Semitoric Polygons |
| title_full | Packing Densities of Delzant and Semitoric Polygons |
| title_fullStr | Packing Densities of Delzant and Semitoric Polygons |
| title_full_unstemmed | Packing Densities of Delzant and Semitoric Polygons |
| title_short | Packing Densities of Delzant and Semitoric Polygons |
| title_sort | packing densities of delzant and semitoric polygons |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212050 |
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