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Stability data, irregular connections and tropical curves

Filippini, S. A.
•
Garcia Fernandez, M.
•
Stoppa, Jacopo
2017
  • journal article

Periodico
SELECTA MATHEMATICA. NEW SERIES
Abstract
We study a class of meromorphic connections nabla(Z) on P^1, parametrised by the central charge Z of a stability condition, with values in a Lie algebra of formal vector fields on a torus. Their definition is motivated by the work of Gaiotto, Moore and Neitzke on wall-crossing and three-dimensional field theories. Our main results concern two limits of the families nabla(Z) as we rescale the central charge Z to RZ. In the R to 0 ``conformal limit'' we recover a version of the connections introduced by Bridgeland and Toledano Laredo (and so the Joyce holomorphic generating functions for enumerative invariants), although with a different construction yielding new explicit formulae. In the R to infty ``large complex structure" limit the connections nabla(Z) make contact with the Gross-Pandharipande-Siebert approach to wall-crossing based on tropical geometry. Their flat sections display tropical behaviour, and also encode certain tropical/relative Gromov-Witten invariants.
DOI
10.1007/s00029-016-0299-x
WOS
WOS:000398491700014
Archivio
http://hdl.handle.net/20.500.11767/15966
info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-84995747118
https://arxiv.org/abs/1403.7404
http://cdsads.u-strasbg.fr/abs/2014arXiv1403.7404F
Diritti
open access
Soggetti
  • Wall-crossing

  • Irregular connection

  • Tropical curves

  • Settore MAT/03 - Geom...

Scopus© citazioni
10
Data di acquisizione
Jun 14, 2022
Vedi dettagli
Web of Science© citazioni
13
Data di acquisizione
Mar 15, 2024
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