Geodesic
The lower bound for the volume of a three-dimensional convex polytope
Algebra and discrete mathematics, Tome 20 (2015) no. 2, pp. 263-285

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In this paper, we provide a lower bound for the volume of a three-dimensional smooth integral convex polytope having interior lattice points. Since our formula has a quite simple form compared with preliminary results, we can easily utilize it for other beneficial purposes. 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.
Keywords: lattice polytopes, polarized varieties, toric varieties
Mots-clés : sectional genus. 
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     author = {Ryo Kawaguchi},
     title = {The lower bound for the volume of a three-dimensional convex polytope},
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Ryo Kawaguchi. The lower bound for the volume of a three-dimensional convex polytope. Algebra and discrete mathematics, Tome 20 (2015) no. 2, pp. 263-285. http://geodesic.mathdoc.fr/item/ADM_2015_20_2_a5/