Witten genus and vanishing results on complete intersections

Chen, Qingtao; Han, Fei; Zhang, Weiping

doi:10.1016/j.crma.2010.02.005

Differential Geometry

Witten genus and vanishing results on complete intersections

Presented by: Jean-Michel Bismut

Chen, Qingtao ¹; Han, Fei ^2,³; Zhang, Weiping ⁴

¹ Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA
² Department of Mathematics, National University of Singapore, 2, Science Drive 2, Singapore 117543, Singapore
³ Department of Mathematics, Stanford University, Stanford, CA, 94305, USA
⁴ Chern Institute of Mathematics & LPMC, Nankai University, Tianjin 300071, PR China

Comptes Rendus. Mathématique, Volume 348 (2010) no. 5-6, pp. 295-298.

Abstract
Résumé

We construct a mod 2 analogue of the Witten genus for $8 k + 2$ dimensional spin manifolds, as well as modular characteristic numbers for a class of ${spin}^{c}$ manifolds which we call ${string}^{c}$ manifolds. When these ${spin}^{c}$ manifolds are actually spin, one recovers the original Witten genus on string manifolds. These genera vanish on string and ${string}^{c}$ complete intersections respectively in complex projective spaces.

Nous construisons un analogue du genre de Witten pour les variétés spins de dimension $8 k + 2$ . Nous construisons aussi des nombres caractéristiques modulaires sur une classe de variétés ${spin}^{c}$ , qu'on appelle variétés ${cordes}^{c}$ . Si les variétés ${cordes}^{c}$ sont spin, on retrouve le genre de Witten sur les variétés cordes. Ces genres sont nuls sur les intersections complètes correspondantes dans les espaces projectives complexes.

Received: 2009-09-14
Accepted: 2010-02-03
Published online: 2010-02-19

DOI: 10.1016/j.crma.2010.02.005

Author's affiliations:

Chen, Qingtao ¹; Han, Fei ^{2, 3}; Zhang, Weiping ⁴

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Chen, Qingtao; Han, Fei; Zhang, Weiping. Witten genus and vanishing results on complete intersections. Comptes Rendus. Mathématique, Volume 348 (2010) no. 5-6, pp. 295-298. doi : 10.1016/j.crma.2010.02.005. https://www.numdam.org/articles/10.1016/j.crma.2010.02.005/

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