Imperial College London
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Professor Richard Thomas FRS

Faculty of Natural Sciences, Department of Mathematics

Royal Society Research Professor (Pure Mathematics)
 
 
 
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Contact

 

richard.thomas Website

 
 
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Location

 

659Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Jiang:2016:jag/690,
author = {Jiang, Y and Thomas, RP},
doi = {jag/690},
journal = {JOURNAL OF ALGEBRAIC GEOMETRY},
pages = {379--397},
title = {VIRTUAL SIGNED EULER CHARACTERISTICS},
url = {http://dx.doi.org/10.1090/jag/690},
volume = {26},
year = {2016}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - Roughly speaking, to any space $ M$ with perfect obstruction theory we associate a space $ N$ with symmetric perfect obstruction theory. It is a cone over $ M$ given by the dual of the obstruction sheaf of $ M$ and contains $ M$ as its zero section. It is locally the critical locus of a function.More precisely, in the language of derived algebraic geometry, to any quasi-smooth space $ M$ we associate its $ (\!-\!1)$-shifted cotangent bundle $ N$.By localising from $ N$ to its  $ \mathbb{C}^$-fixed locus $ M$ this gives five notions of a virtual signed Euler characteristic of $ M$:The Ciocan-Fontanine-Kapranov/Fantechi-Göttsche signed virtual Euler characteristic of $ M$ defined using its own obstruction theory,Graber-Pandharipande's virtual Atiyah-Bott localisation of the virtual cycle of $ N$ to $ M$,Behrend's Kai-weighted Euler characteristic localisation of the virtual cycle of $ N$ to $ M$,Kiem-Li's cosection localisation of the virtual cycle of $ N$ to $ M$,$ (-1)^{\textrm {vd}}$ times by the topological Euler characteristic of $ M$.Our main result is that (1)=(2) and (3)=(4)=(5). The first two are deformation invariant while the last three are not.
AU  - Jiang,Y
AU  - Thomas,RP
DO  - jag/690
EP  - 397
PY  - 2016///
SN  - 1056-3911
SP  - 379
TI  - VIRTUAL SIGNED EULER CHARACTERISTICS
T2  - JOURNAL OF ALGEBRAIC GEOMETRY
UR  - http://dx.doi.org/10.1090/jag/690
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000395426300005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - http://hdl.handle.net/10044/1/48082
VL  - 26
ER  -
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