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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 2015, Volume 20, Issue 2, Pages 263–285 (Mi adm543)

RESEARCH ARTICLE

The lower bound for the volume of a three-dimensional convex polytope

Ryo Kawaguchi

Department of Mathematics, Nara Medical University

Abstract: 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, sectional genus.

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Bibliographic databases:
MSC: Primary 52B20; Secondary 14C20, 14J30, 14M25
Revised: 27.07.2015
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Citation: Ryo Kawaguchi, “The lower bound for the volume of a three-dimensional convex polytope”, Algebra Discrete Math., 20:2 (2015), 263–285

Citation in format AMSBIB
\Bibitem{Kaw15} \by Ryo~Kawaguchi \paper The lower bound for the volume of a three-dimensional convex polytope \jour Algebra Discrete Math. \yr 2015 \vol 20 \issue 2 \pages 263--285 \mathnet{http://mi.mathnet.ru/adm543} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3453816} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000378729300006}