Stable pairs with descendents on local surfaces I: the vertical component

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Title: Stable pairs with descendents on local surfaces I: the vertical component
Authors: Kool, M
Thomas, RP
Item Type: Journal Article
Abstract: We study the full stable pair theory --- with descendents --- of the Calabi-Yau 3-fold $X=K_S$, where $S$ is a surface with a smooth canonical divisor $C$. By both $\mathbb C^*$-localisation and cosection localisation we reduce to stable pairs supported on thickenings of $C$ indexed by partitions. We show that only strict partitions contribute, and give a complete calculation for length-1 partitions. The result is a surprisingly simple closed product formula for these "vertical" thickenings. This gives all contributions for the curve classes $[C]$ and $2[C]$ (and those which are not an integer multiple of the canonical class). Here the result verifies, via the descendent-MNOP correspondence, a conjecture of Maulik-Pandharipande, as well as various results about the Gromov-Witten theory of $S$ and spin Hurwitz numbers.
Issue Date: 21-Dec-2018
Date of Acceptance: 24-Aug-2017
URI: http://hdl.handle.net/10044/1/66449
DOI: https://dx.doi.org/10.4310/PAMQ.2017.v13.n4.a2
ISSN: 1558-8599
Publisher: International Press
Journal / Book Title: Pure and Applied Mathematics Quarterly
Volume: 13
Issue: 4
Copyright Statement: © 2018 by International Press of Boston, Inc. All rights reserved.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
The Royal Society
Funder's Grant Number: EP/G06170X/1
WM100015
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
GROMOV-WITTEN INVARIANTS
DEGREE GW INVARIANTS
REDUCED CLASSES
CYCLES
math.AG
14N35
0101 Pure Mathematics
0102 Applied Mathematics
General Mathematics
Notes: 51 pages, 2 Young diagrams. Appendix by Aaron Pixton and Don Zagier
Publication Status: Published
Online Publication Date: 2017-10-01
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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