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

Liu, Shengxuan

doi:10.1017/fms.2022.96

Cited by 4 publications

(3 citation statements)

References 38 publications

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“…along the boundary ∂U . This, in particular, shows that the weaker version of BMT conjecture proved in [44] for quintic X 5 and in [45] for X 4,2 is sufficient for our result.…”

Section: Discussionsupporting

confidence: 53%

See 1 more Smart Citation

Quantum geometry, stability and modularity

Alexandrov¹,

Feyzbakhsh²,

Klemm³

et al. 2023

Preprint

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By exploiting new mathematical relations between Pandharipande-Thomas (PT) invariants, closely related to Gopakumar-Vafa (GV) invariants, and rank 0 Donaldson-Thomas (DT) invariants counting D4-D2-D0 BPS bound states, we rigorously compute the first few terms in the generating series of Abelian D4-D2-D0 indices for compact one-parameter Calabi-Yau threefolds of hypergeometric type. In all cases where GV invariants can be computed to sufficiently high genus, we find striking confirmation that the generating series is modular, and predict infinite series of Abelian D4-D2-D0 indices. Conversely, we use these results to provide new constraints for the direct integration method, which allows to compute GV invariants (and therefore the topological string partition function) to higher genus than hitherto possible. The triangle of relations between GV/PT/DT invariants is powered by a new explicit formula relating PT and rank 0 DT invariants, which is proven in an Appendix by the second named author. As a corollary, we obtain rigorous Castelnuovo-type bounds for PT and GV invariants for CY threefolds with Picard rank one.

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“…along the boundary ∂U . This, in particular, shows that the weaker version of BMT conjecture proved in [44] for quintic X 5 and in [45] for X 4,2 is sufficient for our result.…”

Section: Discussionsupporting

confidence: 53%

“…The conjectural BMT inequality (2.38) has now been proved for the quintic threefold X 5 and for a degree (4, 2) complete intersection X 4,2 in P 5 when (b, w) satisfy [44,45] (2.40)…”

Section: 2mentioning

confidence: 95%

Quantum geometry, stability and modularity

Alexandrov¹,

Feyzbakhsh²,

Klemm³

et al. 2023

Preprint

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“…• X is one of the Calabi-Yau threefolds considered in [Kos22]; with some work, one can show the weakening of Conjecture 2.3 proved in [Kos22, Theorem 1.2] is still strong enough to give Theorem 1 for n 0, and • X is a quintic threefold (see [Li19a]), or a (2,4) complete intersection in P 5 (see [Liu22]), and (b, w) are described below.…”

Section: Weak Stability Conditionsmentioning

confidence: 99%

Curve counting and S-duality

Feyzbakhsh¹,

Thomas²

2023

Épijournal De Géométrie Algébrique

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We work on a projective threefold $X$ which satisfies the Bogomolov-Gieseker conjecture of Bayer-Macr\`i-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.

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Stability conditions on Calabi-Yau double/triple solids

Koseki

2022

Forum of Mathematics, Sigma

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In this paper, we prove a stronger form of the Bogomolov–Gieseker (BG) inequality for stable sheaves on two classes of Calabi–Yau threefolds, namely, weighted hypersurfaces inside the weighted projective spaces $\mathbb {P}(1, 1, 1, 1, 2)$ and $\mathbb {P}(1, 1, 1, 1, 4)$ . Using the stronger BG inequality as a main technical tool, we construct open subsets in the spaces of Bridgeland stability conditions on these Calabi–Yau threefolds.

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

Cited by 4 publications

References 38 publications

Quantum geometry, stability and modularity

Quantum geometry, stability and modularity

Curve counting and S-duality

Stability conditions on Calabi-Yau double/triple solids

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