Abstract.
We derive a classification algorithm for reflexive simplices in arbitrary fixed dimension. It is based on the assignment of a weight Q ? ℕn+1 to an integral n-simplex, the construction, up to an isomorphism, of all simplices with given weight Q, and the characterization in terms of the weight as to when a simplex with reduced weight is reflexive. This also yields a convex-geometric reproof of the characterization in terms of weights for weighted projective spaces to have at most Gorenstein singularities.
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Received: 30 March 1999 / Revised version: 18 October 2001
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Conrads, H. Weighted projective spaces and reflexive simplices. Manuscripta Math. 107, 215–227 (2002). https://doi.org/10.1007/s002290100235
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DOI: https://doi.org/10.1007/s002290100235