Imperial College London
Portrait Picture

Professor Richard Thomas FRS

Faculty of Natural Sciences, Department of Mathematics

Royal Society Research Professor (Pure Mathematics)
 
 
 
//

Contact

 

richard.thomas Website

 
 
//

Location

 

659Huxley BuildingSouth Kensington Campus

//

Summary

 

Publications

Citation

BibTex format

@article{Gholampour:2019:10.2140/tunis.2020.2.633,
author = {Gholampour, A and Thomas, RP},
doi = {10.2140/tunis.2020.2.633},
journal = {Tunisian Journal of Mathematics},
pages = {633--665},
title = {Degeneracy loci, virtual cycles and nested Hilbert schemes I},
url = {http://dx.doi.org/10.2140/tunis.2020.2.633},
volume = {2},
year = {2019}
}
Download

RIS format (EndNote, RefMan)

TY  - JOUR
AB  - Given a map of vector bundles on a smooth variety, consider the deepestdegeneracy locus where its rank is smallest. We show it carries a naturalperfect obstruction theory whose virtual cycle can be calculated by theThom-Porteous formula.  We show nested Hilbert schemes of points on surfaces can be expressed asdegeneracy loci. We show how to modify the resulting obstruction theories torecover the virtual cycles of Vafa-Witten and reduced local DT theories.  The result computes some Vafa-Witten invariants in terms of Carlsson-Okounkovoperators. This proves and extends a conjecture of Gholampour-Sheshmani-Yau andgeneralises a vanishing result of Carlsson-Okounkov.
AU  - Gholampour,A
AU  - Thomas,RP
DO  - 10.2140/tunis.2020.2.633
EP  - 665
PY  - 2019///
SN  - 2576-7658
SP  - 633
TI  - Degeneracy loci, virtual cycles and nested Hilbert schemes I
T2  - Tunisian Journal of Mathematics
UR  - http://dx.doi.org/10.2140/tunis.2020.2.633
UR  - http://arxiv.org/abs/1709.06105v2
UR  - http://hdl.handle.net/10044/1/73934
VL  - 2
ER  -
Download