Reflexive polyhedra, weights and toric CalabiYau fibrations
Abstract
During the last years we have generated a large number of data related to CalabiYau hypersurfaces in toric varieties which can be described by reflexive polyhedra. We classified all reflexive polyhedra in three dimensions leading to K3 hypersurfaces and have nearly completed the four dimensional case relevant to CalabiYau threefolds. In addition, we have analysed for many of the resulting spaces whether they allow fibration structures of the types that are relevant in the context of superstring dualities. In this survey we want to give background information both on how we obtained these data, which can be found at our web site, and on how they may be used. We give a complete exposition of our classification algorithm at a mathematical (rather than algorithmic) level. We also describe how fibration structures manifest themselves in terms of toric diagrams and how we managed to find the respective data. Both for our classification scheme and for simple descriptions of fibration structures the concept of weight systems plays an important role.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2000
 arXiv:
 arXiv:math/0001106
 Bibcode:
 2000math......1106K
 Keywords:

 Algebraic Geometry;
 14M25;
 14J32;
 81T30
 EPrint:
 36 pages, LaTeX2e