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@article{Pandharipande:2016:10.4310/SDG.2016.v21.n1.a7,
author = {Pandharipande, R and Thomas, RP},
doi = {10.4310/SDG.2016.v21.n1.a7},
journal = {Surveys in Differential Geometry},
pages = {289--311},
title = {Notes on the proof of the KKV conjecture},
url = {http://dx.doi.org/10.4310/SDG.2016.v21.n1.a7},
volume = {21},
year = {2016}
}

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TY  - JOUR
AB  - The Katz-Klemm-Vafa conjecture expresses the GromovWittentheory of K3 surfaces (and K3-fibred 3-folds in fibre classes)in terms of modular forms. Its recent proof gives the first non-toricgeometry in dimension greater than 1 where Gromov-Witten theory isexactly solved in all genera.We survey the various steps in the proof. The MNOP correspondenceand a new Pairs/Noether-Lefschetz correspondence for K3-fibred3-folds transform the Gromov-Witten problem into a calculation of thefull stable pairs theory of a local K3-fibred 3-fold. The stable pairs calculation is then carried out via degeneration, localisation, vanishing results, and new multiple cover formulae.
AU  - Pandharipande,R
AU  - Thomas,RP
DO  - 10.4310/SDG.2016.v21.n1.a7
EP  - 311
PY  - 2016///
SN  - 2164-4713
SP  - 289
TI  - Notes on the proof of the KKV conjecture
T2  - Surveys in Differential Geometry
UR  - http://dx.doi.org/10.4310/SDG.2016.v21.n1.a7
UR  - http://hdl.handle.net/10044/1/32991
VL  - 21
ER  -

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