Journal of Differential Geometry

Generalized Witten Genus and Vanishing Theorems

Qingtao Chen, Fei Han, and Weiping Zhang

Full-text: Open access


We construct a generalized Witten genus for spin$^c$ manifolds, which takes values in level 1 modular forms with integral Fourier expansion on a class of spin manifolds called string$^c$ manifolds. We also construct a mod 2 analogue of the Witten genus for $8k+2$ dimensional spin manifolds. The Landweber-Stong type vanishing theorems are proven for the generalizedWitten genus and the mod 2 Witten genus on string$^c$ and string (generalized) complete intersections in (product of) complex projective spaces respectively.

Article information

J. Differential Geom., Volume 88, Number 1 (2011), 1-39.

First available in Project Euclid: 4 October 2011

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Chen, Qingtao; Han, Fei; Zhang, Weiping. Generalized Witten Genus and Vanishing Theorems. J. Differential Geom. 88 (2011), no. 1, 1--39. doi:10.4310/jdg/1317758867.

Export citation