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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| Datum: | 2016 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2016
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/15 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543423256854528 |
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| author | Kawaguchi, Ryo |
| author_facet | Kawaguchi, Ryo |
| author_sort | Kawaguchi, Ryo |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2016-01-12T07:40:37Z |
| 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. |
| first_indexed | 2026-02-08T07:59:18Z |
| format | Article |
| id | admjournalluguniveduua-article-15 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:59:18Z |
| publishDate | 2016 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| 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 |
| 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 |
| topic | Lattice polytopes polarized varieties toric varieties sectional genus 52B20 14C20 14J30 14M25 |
| topic_facet | Lattice polytopes polarized varieties toric varieties sectional genus 52B20 14C20 14J30 14M25 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/15 |
| work_keys_str_mv | AT kawaguchiryo thelowerboundforthevolumeofathreedimensionalconvexpolytope AT kawaguchiryo lowerboundforthevolumeofathreedimensionalconvexpolytope |