# Curve counting and S-duality

@article{Feyzbakhsh2020CurveCA, title={Curve counting and S-duality}, author={Soheyla Feyzbakhsh and Richard P. Thomas}, journal={arXiv: Algebraic Geometry}, year={2020} }

We work on a projective threefold $X$ which satisfies the Bogomolov-Gieseker conjecture of Bayer-Macri-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…

## 6 Citations

On the Bogomolov-Gieseker inequality for hypersurfaces in the projective spaces

- Mathematics
- 2020

We investigate the stronger form of the Bogomolov-Gieseker inequality on smooth hypersurfaces in the projective space of any degree and dimension. The main technical tool is the theory of…

Explicit formulae for rank zero DT invariants and the OSV conjecture

- Mathematics
- 2022

. Fix a Calabi-Yau 3-fold X satisfying the Bogomolov-Gieseker conjecture of Bayer-Macr`ı-Toda, such as the quintic 3-fold. By two diﬀerent wall-crossing arguments we prove two diﬀerent explicit…

Modular bootstrap for D4-D2-D0 indices on compact Calabi-Yau threefolds

- Mathematics
- 2022

: We investigate the modularity constraints on the generating series h r ( τ ) of BPS indices counting D4-D2-D0 bound states with ﬁxed D4-brane charge r in type IIA string theory compactiﬁed on…

Scaling black holes and modularity

- PhysicsJournal of High Energy Physics
- 2022

Abstract
Scaling black holes are solutions of supergravity with multiple black hole singularities, which can be adiabatically connected to a single center black hole solution. We develop techniques…

Stability condition on Calabi-Yau threefold of complete intersection of quadratic and quartic hypersurfaces

- Mathematics
- 2021

In this paper, we prove a Clifford type inequality for the curve X2,2,2,4, which is the intersection of a quartic and three general quadratics in P. We thus prove a stronger Bogomolov–Gieseker…

An Application of Wall-Crossing to Noether–Lefschetz Loci

- Mathematics
- 2019

Consider a smooth projective 3-fold $X$ satisfying the Bogomolov-Gieseker conjecture of Bayer-Macri-Toda (such as $\mathbb P^3$, the quintic threefold or an abelian threefold).
Let $L$ be a line…

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