## On the rigidity theorem for elliptic genera

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- by Anand Dessai and Rainer Jung PDF
- Trans. Amer. Math. Soc.
**350**(1998), 4195-4220 Request permission

## Abstract:

We give a detailed proof of the rigidity theorem for elliptic genera. Using the Lefschetz fixed point formula we carefully analyze the relation between the characteristic power series defining the elliptic genera and the equivariant elliptic genera. We show that equivariant elliptic genera converge to Jacobi functions which are holomorphic. This implies the rigidity of elliptic genera. Our approach can be easily modified to give a proof of the rigidity theorem for the elliptic genera of level $N$.## References

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## Additional Information

**Anand Dessai**- Affiliation: Department of Mathematics University of Mainz 55099 Mainz Germany
- Address at time of publication: Department of Mathematics University of Augsburg 86135 Augsburg Germany
- MR Author ID: 630872
- Email: dessai@mathpool.Uni-Augsburg.DE
**Rainer Jung**- Affiliation: Mathematisches Forschungsinstitut Oberwolfach Lorenzenhof 77709 Oberwolfach Germany
- Email: jung@MFO.DE
- Received by editor(s): January 7, 1997
- © Copyright 1998 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**350**(1998), 4195-4220 - MSC (1991): Primary 58G10, 19L47, 11F03; Secondary 57S15, 13N10
- DOI: https://doi.org/10.1090/S0002-9947-98-02321-6
- MathSciNet review: 1608301