A Note on the Formal Groups of Weighted Delsarte Threefolds
One-dimensional formal groups over an algebraically closed field of positive characteristic are classified by their height. In the case of K3 surfaces, the height of their formal groups takes integer values between 1 and 10 or ∞. For Calabi-Yau threefolds, the height is bounded by h¹'² + 1 if i...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2018 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2018
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209860 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | A Note on the Formal Groups of Weighted Delsarte Threefolds / Y. Goto // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 20 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-209860 |
|---|---|
| record_format |
dspace |
| spelling |
Goto, Y. 2025-11-27T14:58:47Z 2018 A Note on the Formal Groups of Weighted Delsarte Threefolds / Y. Goto // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 20 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 14L05; 14J32 arXiv: 1805.04233 https://nasplib.isofts.kiev.ua/handle/123456789/209860 https://doi.org/10.3842/SIGMA.2018.097 One-dimensional formal groups over an algebraically closed field of positive characteristic are classified by their height. In the case of K3 surfaces, the height of their formal groups takes integer values between 1 and 10 or ∞. For Calabi-Yau threefolds, the height is bounded by h¹'² + 1 if it is finite, where h¹'² is a Hodge number. At present, there are only a limited number of concrete examples for explicit values or the distribution of the height. In this paper, we consider Calabi-Yau threefolds arising from weighted Delsarte threefolds in positive characteristic. We describe an algorithm for computing the height of their formal groups and carry out calculations with various Calabi-Yau threefolds of Delsarte type. While the author was preparing for this manuscript, he visited Noriko Yui several times at the Department of Mathematics and Statistics of Queen’s University and at the Fields Institute in Canada. He thanks Professor Yui for many inspiring discussions and is grateful to the two institutions for their hospitality. The author also thanks the Banff International Research Station in Canada for the workshop on Modular Forms in String Theory in 2016, where the main result of this paper was presented. Many thanks are due to the referees of the paper for their useful comments and suggestions. This work was supported partially by the NSERC Discovery Grant of Noriko Yui at Queen’s University in Canada and by the author’s JSPS Grant-in-Aid for Scientific Research (C) 15540001 and 15K04771. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Note on the Formal Groups of Weighted Delsarte Threefolds Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
A Note on the Formal Groups of Weighted Delsarte Threefolds |
| spellingShingle |
A Note on the Formal Groups of Weighted Delsarte Threefolds Goto, Y. |
| title_short |
A Note on the Formal Groups of Weighted Delsarte Threefolds |
| title_full |
A Note on the Formal Groups of Weighted Delsarte Threefolds |
| title_fullStr |
A Note on the Formal Groups of Weighted Delsarte Threefolds |
| title_full_unstemmed |
A Note on the Formal Groups of Weighted Delsarte Threefolds |
| title_sort |
note on the formal groups of weighted delsarte threefolds |
| author |
Goto, Y. |
| author_facet |
Goto, Y. |
| publishDate |
2018 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
One-dimensional formal groups over an algebraically closed field of positive characteristic are classified by their height. In the case of K3 surfaces, the height of their formal groups takes integer values between 1 and 10 or ∞. For Calabi-Yau threefolds, the height is bounded by h¹'² + 1 if it is finite, where h¹'² is a Hodge number. At present, there are only a limited number of concrete examples for explicit values or the distribution of the height. In this paper, we consider Calabi-Yau threefolds arising from weighted Delsarte threefolds in positive characteristic. We describe an algorithm for computing the height of their formal groups and carry out calculations with various Calabi-Yau threefolds of Delsarte type.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/209860 |
| citation_txt |
A Note on the Formal Groups of Weighted Delsarte Threefolds / Y. Goto // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 20 назв. — англ. |
| work_keys_str_mv |
AT gotoy anoteontheformalgroupsofweighteddelsartethreefolds AT gotoy noteontheformalgroupsofweighteddelsartethreefolds |
| first_indexed |
2025-12-07T18:21:11Z |
| last_indexed |
2025-12-07T18:21:11Z |
| _version_ |
1850886112066666496 |