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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| Date: | 2016 |
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| Language: | English |
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Lugansk National Taras Shevchenko University
2016
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/15 |
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| Journal Title: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-152016-01-12T07:40:37Z The lower bound for the volume of a three-dimensional convex polytope Kawaguchi, Ryo Lattice polytopes, polarized varieties, toric varieties, sectional genus 52B20; 14C20; 14J30; 14M25 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. Lugansk National Taras Shevchenko University 2016-01-12 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/15 Algebra and Discrete Mathematics; Vol 20, No 2 (2015) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/15/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/15/32 Copyright (c) 2016 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2016-01-12T07:40:37Z |
| collection |
OJS |
| language |
English |
| topic |
Lattice polytopes polarized varieties toric varieties sectional genus 52B20 14C20 14J30 14M25 |
| spellingShingle |
Lattice polytopes polarized varieties toric varieties sectional genus 52B20 14C20 14J30 14M25 Kawaguchi, Ryo The lower bound for the volume of a three-dimensional convex polytope |
| topic_facet |
Lattice polytopes polarized varieties toric varieties sectional genus 52B20 14C20 14J30 14M25 |
| format |
Article |
| author |
Kawaguchi, Ryo |
| author_facet |
Kawaguchi, Ryo |
| author_sort |
Kawaguchi, Ryo |
| title |
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_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 |
| 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2016 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/15 |
| work_keys_str_mv |
AT kawaguchiryo thelowerboundforthevolumeofathreedimensionalconvexpolytope AT kawaguchiryo lowerboundforthevolumeofathreedimensionalconvexpolytope |
| first_indexed |
2025-07-17T10:33:27Z |
| last_indexed |
2025-07-17T10:33:27Z |
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1837889914192003072 |