Curve counting and S-duality
Épijournal de Géométrie Algébrique, Tome 7 (2023)
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We work on a projective threefold $X$ which satisfies the Bogomolov-Gieseker conjecture of Bayer-Macrì-Toda, such as $\mathbb P^3$ or the quintic threefold. We prove certain moduli spaces of 2-dimensional torsion sheaves on $X$ are smooth bundles over Hilbert schemes of ideal sheaves of curves and points in $X$. When $X$ is Calabi-Yau this gives a simple wall crossing formula expressing curve counts (and so ultimately Gromov-Witten invariants) in terms of counts of D4-D2-D0 branes. These latter invariants are predicted to have modular properties which we discuss from the point of view of S-duality and Noether-Lefschetz theory.
@article{10_46298_epiga_2023_volume7_9818,
author = {Feyzbakhsh, Soheyla and Thomas, Richard P.},
title = {Curve counting and {S-duality}},
journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
publisher = {mathdoc},
volume = {7},
year = {2023},
doi = {10.46298/epiga.2023.volume7.9818},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2023.volume7.9818/}
}
TY - JOUR AU - Feyzbakhsh, Soheyla AU - Thomas, Richard P. TI - Curve counting and S-duality JO - Épijournal de Géométrie Algébrique PY - 2023 VL - 7 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.46298/epiga.2023.volume7.9818/ DO - 10.46298/epiga.2023.volume7.9818 LA - en ID - 10_46298_epiga_2023_volume7_9818 ER -
%0 Journal Article %A Feyzbakhsh, Soheyla %A Thomas, Richard P. %T Curve counting and S-duality %J Épijournal de Géométrie Algébrique %D 2023 %V 7 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.46298/epiga.2023.volume7.9818/ %R 10.46298/epiga.2023.volume7.9818 %G en %F 10_46298_epiga_2023_volume7_9818
Feyzbakhsh, Soheyla; Thomas, Richard P. Curve counting and S-duality. Épijournal de Géométrie Algébrique, Tome 7 (2023). doi: 10.46298/epiga.2023.volume7.9818
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