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Mosc. Math. J., 2010, Volume 10, Number 2, Pages 285–316 (Mi mmj381)  

This article is cited in 4 scientific papers (total in 4 papers)

Classification of Gorenstein toric Del Pezzo varieties in arbitrary dimension

Victor Batyrev, Dorothee Juny

Mathematisches Institut, Universität Tübingen, Tübingen, Germany

Abstract: An $n$-dimensional Gorenstein toric Fano variety $X$ is called Del Pezzo variety if the anticanonical class $-K_X$ is an $(n-1)$-multiple of a Cartier divisor. Our purpose is to give a complete biregular classfication of Gorenstein toric Del Pezzo varieties in arbitrary dimension $n\ge2$. We show that up to isomorphism there exist exactly 37 Gorenstein toric Del Pezzo varieties of dimension $n$ which are not cones over $(n-1)$-dimensional Gorenstein toric Del Pezzo varieties. Our results are closely related to the classification of all Minkowski sum decompositions of reflexive polygons due to Emiris and Tsigaridas and to the classification up to deformation of $n$-dimensional almost Del Pezzo manifolds obtained by Jahnke and Peternell.

Key words and phrases: toric varieties, Fano varieties, lattice polytopes.

DOI: https://doi.org/10.17323/1609-4514-2010-10-2-285-316

Full text: http://www.ams.org/.../abst10-2-2010.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 14M25, 14J45, 52B20
Received: March 29, 2009
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Citation: Victor Batyrev, Dorothee Juny, “Classification of Gorenstein toric Del Pezzo varieties in arbitrary dimension”, Mosc. Math. J., 10:2 (2010), 285–316

Citation in format AMSBIB
\Bibitem{BatJun10}
\by Victor~Batyrev, Dorothee~Juny
\paper Classification of Gorenstein toric Del Pezzo varieties in arbitrary dimension
\jour Mosc. Math.~J.
\yr 2010
\vol 10
\issue 2
\pages 285--316
\mathnet{http://mi.mathnet.ru/mmj381}
\crossref{https://doi.org/10.17323/1609-4514-2010-10-2-285-316}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2722799}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000279342400002}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Cherkis S.A., “Phases of Five-Dimensional Theories, Monopole Walls, and Melting Crystals”, J. High Energy Phys., 2014, no. 6, 027  crossref  mathscinet  isi  elib  scopus
    2. Lorenz B., Nill B., “on Smooth Gorenstein Polytopes”, Tohoku Math. J., 67:4 (2015), 513–530  crossref  mathscinet  zmath  isi
    3. Batyrev V., Schaller K., “Stringy Chern Classes of Singular Toric Varieties and Their Applications”, Commun. Number Theory Phys., 11:1 (2017), 1–40  crossref  mathscinet  zmath  isi
    4. Tsuchiya A., “Gorenstein Simplices and the Associated Finite Abelian Groups”, Eur. J. Comb., 67 (2018), 145–157  crossref  mathscinet  zmath  isi  scopus
  • Moscow Mathematical Journal
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