Invariance Property of Orbifold Elliptic Genus for Multi-Fans
نویسندگان
چکیده
The complex elliptic genus was first introduced by Witten [21] and then studied by several authors such as Hirzebruch [13], Bott and Taubes [5] mainly in connection with its rigidity property. It was further generalized in two ways; one way to complex orbifolds and the other to singular projective varieties. Generalization to singular varieties was given by Borisov-Libgober [3], [4]. They called it singular elliptic genus; it is defined for Kawamata-log-terminal pairs (X,D) of a variety X and a Q-divisor D. We shall denote it by Ellsing(X,D). It has an invariant property with respect to blow-ups. Namely, if f : X̃ → X is a blow-up along a non-singular locus in X which is normal crossing to Supp(D) and D̃ is a divisor on X̃ such that KX̃ + D̃ = f (KX +D), then
منابع مشابه
Elliptic Genera, Torus Orbifolds and Multi-fans; Ii
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