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Abstract

We investigate Gorenstein toric Fano varieties by combinatorial methods using the notion of a reflexive polytope which appeared in connection to mirror symmetry. The paper contains generalizations of tools and previously known results for nonsingular toric Fano varieties. As applications we obtain new classification results, bounds of invariants and formulate conjectures concerning combinatorial and geometrical properties of reflexive polytopes.
Mathematics Subject Classification (2000): 14J45, 14M25, 52B20
Acknowledgement The author would like to thank his thesis advisor Professor Victor Batyrev for posing problems, his advice and encouragement, as well as Professor Günter Ewald for giving reference to [Wir97] and Professor Klaus Altmann for the possibility of giving a talk at the FU Berlin. The author would also like to thank Professor Maximilian Kreuzer for the support with the computer package PALP, the classification data and many examples. Finally the author is grateful to the anonymous referee for corrections and many useful suggestions. The author was supported by DFG, Forschungsschwerpunkt ldquoGlobale Methoden in der komplexen Geometrierdquo. This work is part of the authorrsquos thesis.

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