Abstract
F-theory, as Theory of Everything is compactified on Calabi-Yau threefolds or fourfolds. Using toric approximation of Batyrev and mirror symmetry of Calabi-Yau manifolds it is possible to present Calabi-Yau in the form of dual integer polyhedra. With the help of Gelfand, Zelevinsky, Kapranov algorithm were calculated the numbers of BPS-states in F-theory, and by application of Tate algorithm were determined the enhanced symmetries. As the result, any integral dual polyhedron representing a Calabi-Yau manifold, is characterized by its own set of topological invariants - the numbers of BPS states, whose central charges are classified by enhanced symmetries.
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