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@article{Kool:2018:10.4310/PAMQ.2017.v13.n4.a2,
author = {Kool, M and Thomas, RP},
doi = {10.4310/PAMQ.2017.v13.n4.a2},
journal = {Pure and Applied Mathematics Quarterly},
title = {Stable pairs with descendents on local surfaces I: the vertical component},
url = {http://dx.doi.org/10.4310/PAMQ.2017.v13.n4.a2},
volume = {13},
year = {2018}
}

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TY  - JOUR
AB  - We study the full stable pair theory --- with descendents --- of theCalabi-Yau 3-fold $X=K_S$, where $S$ is a surface with a smooth canonicaldivisor $C$.  By both $\mathbb C^$-localisation and cosection localisation we reduce tostable pairs supported on thickenings of $C$ indexed by partitions. We showthat only strict partitions contribute, and give a complete calculation forlength-1 partitions. The result is a surprisingly simple closed product formulafor these "vertical" thickenings.  This gives all contributions for the curve classes $[C]$ and $2[C]$ (andthose which are not an integer multiple of the canonical class). Here theresult verifies, via the descendent-MNOP correspondence, a conjecture ofMaulik-Pandharipande, as well as various results about the Gromov-Witten theoryof $S$ and spin Hurwitz numbers.
AU  - Kool,M
AU  - Thomas,RP
DO  - 10.4310/PAMQ.2017.v13.n4.a2
PY  - 2018///
SN  - 1558-8599
TI  - Stable pairs with descendents on local surfaces I: the vertical component
T2  - Pure and Applied Mathematics Quarterly
UR  - http://dx.doi.org/10.4310/PAMQ.2017.v13.n4.a2
UR  - http://arxiv.org/abs/1605.02576v1
UR  - http://hdl.handle.net/10044/1/66449
VL  - 13
ER  -

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