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Vanishing theorems of generalized Witten genus for generalized complete intersections in flag manifolds

Xiaobo Zhuang

Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027, P. R. China

https://doi.org/10.1142/S0129167X16500762Cited by:1 (Source: Crossref)

Abstract

We propose a potential function $W$ for the cohomology ring of partial flag manifolds. We prove a formula expressing integrals over partial flag manifolds by residues, which generalizes [E. Witten, The Verlinde algebra and the cohomology of the Grassmannian, in Geometry, Topology, Physics (International Press, 1995), pp. 357–422]. Using this formula, we prove a Landweber–Stong type vanishing theorem for generalized ${string}^{c}$ complete intersections in flag manifolds, which serves as evidence for the ${string}^{c}$ version of Stolz conjecture [Q. Chen, F. Han and W. Zhang, Generalized Witten genus and vanishing theorems, J. Differential Geom.88(1) (2011) 1–39].

Keywords:

AMSC: 58J26, 14K25, 14M15

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