Elliptic genera of level N for complete intersections

Abstract

We focus on the elliptic genera of level N at the cusps of a congruence subgroup for any complete intersection. Writing the first Chern class of a complete intersection as a product of an integral coefficient c₁ and a generator of the 2nd integral cohomology group, we mainly discuss the values of the elliptic genera of level N for the complete intersection in the cases of c₁>, =, or<0, In particular, the values about the Todd genus, \widehat{A}\mathrm{-genus}, and A_k-genus can be derived from the elliptic genera of level N.

Keywords

Complete intersection, elliptic genera of level N / Todd genus, A_k-genus

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