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{Katz:2016:10.1007/978-3-319-29959-4_6,
author = {Katz, S and Klemm, A and Pandharipande, R and Thomas, RP},
doi = {10.1007/978-3-319-29959-4_6},
pages = {111--146},
title = {On the motivic stable pairs invariants of K3 surfaces},
url = {http://dx.doi.org/10.1007/978-3-319-29959-4_6},
volume = {315},
year = {2016}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - For a K3 surface S and a class β ∈ Pic(S), we study motivic invariants of stable pairs moduli spaces associated to 3-fold thickenings of S. We conjecture suitable deformation and divisibility invariances for the Betti realization. Our conjectures, together with earlier calculations of Kawai-Yoshioka, imply a full determination of the theory in terms of the Hodge numbers of the Hilbert schemes of points of S. The work may be viewed as the third in a sequence of formulas starting with Yau-Zaslow and Katz-Klemm-Vafa (each recovering the former). Numerical data suggest the motivic invariants are linked to the Mathieu M24 moonshine phenomena. The KKV formula and the Pairs/Noether-Lefschetz correspondence together determine the BPS counts of K3-fibered Calabi-Yau 3-folds in fiber classes in terms of modular forms. We propose a framework for a refined P/NL correspondence for the motivic invariants of K3-fibered CY 3-folds. For the STU model, a complete conjecture is presented.
AU  - Katz,S
AU  - Klemm,A
AU  - Pandharipande,R
AU  - Thomas,RP
DO  - 10.1007/978-3-319-29959-4_6
EP  - 146
PY  - 2016///
SN  - 0743-1643
SP  - 111
TI  - On the motivic stable pairs invariants of K3 surfaces
UR  - http://dx.doi.org/10.1007/978-3-319-29959-4_6
VL  - 315
ER  -
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