The lower bound for the volume of a three-dimensional convex polytope
In this paper, we provide a lower bound for the volume of a three-dimensional smooth integral convex polytope having interior lattice points. Our formula has a quite simple form compared with preliminary results. Therefore, we can easily utilize it for other beneficial purposes. Firstly, as an immed...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2015 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2015
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/155139 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The lower bound for the volume of a three-dimensional convex polytope / R. Kawaguchi // Algebra and Discrete Mathematics. — 2015. — Vol. 20, № 2. — С. 263-285. — Бібліогр.: 17 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862735292702654464 |
|---|---|
| author | Kawaguchi, R. |
| author_facet | Kawaguchi, R. |
| citation_txt | The lower bound for the volume of a three-dimensional convex polytope / R. Kawaguchi // Algebra and Discrete Mathematics. — 2015. — Vol. 20, № 2. — С. 263-285. — Бібліогр.: 17 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | In this paper, we provide a lower bound for the volume of a three-dimensional smooth integral convex polytope having interior lattice points. Our formula has a quite simple form compared with preliminary results. Therefore, we can easily utilize it for other beneficial purposes. Firstly, as an immediate consequence of our lower bound, we obtain a characterization of toric Fano threefold. Besides, we compute the sectional genus of a three-dimensional polarized toric variety, and classify toric Castelnuovo varieties.
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| first_indexed | 2025-12-07T19:48:05Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-155139 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T19:48:05Z |
| publishDate | 2015 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Kawaguchi, R. 2019-06-16T09:40:36Z 2019-06-16T09:40:36Z 2015 The lower bound for the volume of a three-dimensional convex polytope / R. Kawaguchi // Algebra and Discrete Mathematics. — 2015. — Vol. 20, № 2. — С. 263-285. — Бібліогр.: 17 назв. — англ. 1726-3255 2010 MSC:Primary 52B20; Secondary 14C20, 14J30, 14M25. https://nasplib.isofts.kiev.ua/handle/123456789/155139 In this paper, we provide a lower bound for the volume of a three-dimensional smooth integral convex polytope having interior lattice points. Our formula has a quite simple form compared with preliminary results. Therefore, we can easily utilize it for other beneficial purposes. Firstly, as an immediate consequence of our lower bound, we obtain a characterization of toric Fano threefold. Besides, we compute the sectional genus of a three-dimensional polarized toric variety, and classify toric Castelnuovo varieties. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics The lower bound for the volume of a three-dimensional convex polytope Article published earlier |
| spellingShingle | The lower bound for the volume of a three-dimensional convex polytope Kawaguchi, R. |
| title | The lower bound for the volume of a three-dimensional convex polytope |
| title_full | The lower bound for the volume of a three-dimensional convex polytope |
| title_fullStr | The lower bound for the volume of a three-dimensional convex polytope |
| title_full_unstemmed | The lower bound for the volume of a three-dimensional convex polytope |
| title_short | The lower bound for the volume of a three-dimensional convex polytope |
| title_sort | lower bound for the volume of a three-dimensional convex polytope |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155139 |
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