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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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2015 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2015
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| Online Zugang: | 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 |
| Zitieren: | 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. |
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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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
The lower bound for the volume of a three-dimensional convex polytope |
| spellingShingle |
The lower bound for the volume of a three-dimensional convex polytope Kawaguchi, R. |
| title_short |
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_sort |
lower bound for the volume of a three-dimensional convex polytope |
| author |
Kawaguchi, R. |
| author_facet |
Kawaguchi, R. |
| publishDate |
2015 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/155139 |
| 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. |
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AT kawaguchir thelowerboundforthevolumeofathreedimensionalconvexpolytope AT kawaguchir lowerboundforthevolumeofathreedimensionalconvexpolytope |
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2025-12-07T19:48:05Z |
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2025-12-07T19:48:05Z |
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1850880174463123456 |