Witten genus and vanishing results on complete intersections

Qingtao Chen; Fei Han; Weiping Zhang

doi:10.1016/j.crma.2010.02.005

Witten genus and vanishing results on complete intersections

Qingtao Chen, Fei Han, Weiping Zhang

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Pages (from-to)	295-298
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	348
Issue number	5-6
DOIs	https://doi.org/10.1016/j.crma.2010.02.005
State	Published - Mar 2010

ASJC Scopus subject areas

General Mathematics

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title = "Witten genus and vanishing results on complete intersections",

abstract = "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 spinc manifolds which we call stringc manifolds. When these spinc manifolds are actually spin, one recovers the original Witten genus on string manifolds. These genera vanish on string and stringc complete intersections respectively in complex projective spaces.",

author = "Qingtao Chen and Fei Han and Weiping Zhang",

note = "Funding Information: We would like to thank Kefeng Liu for very helpful discussions. The work of the second author was partially supported by a start-up grant from National University of Singapore. The work of the third author was partially supported by NNSFC and MOEC.",

year = "2010",

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AU - Han, Fei

AU - Zhang, Weiping

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PY - 2010/3

Y1 - 2010/3

N2 - 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 spinc manifolds which we call stringc manifolds. When these spinc manifolds are actually spin, one recovers the original Witten genus on string manifolds. These genera vanish on string and stringc complete intersections respectively in complex projective spaces.

AB - 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 spinc manifolds which we call stringc manifolds. When these spinc manifolds are actually spin, one recovers the original Witten genus on string manifolds. These genera vanish on string and stringc complete intersections respectively in complex projective spaces.

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ER -

Witten genus and vanishing results on complete intersections

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