Abstract
Multi-fan is an analogous notion of fan in toric theory. Fan is a combinatorial object associated to a toric variety. Multi-fan is associated to an orbifold with an action of half the dimension of the orbifold. In this paper the equivariant elliptic genus and the equivariant orbifold elliptic genus of multi-fans are defined and their character formulas are exhibited. A vanishing theorem concerning elliptic genus of multi-fans of global type and its applications to toric varieties are given.
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