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The stability manifold of $E{\times} E{\times} E$

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arxiv 2410.08028 v1 pith:FETCQAAN submitted 2024-10-10 math.AG hep-thmath.SG

Fabian Haiden , Benjamin Sung This is my paper · ORCID
classification math.AGhep-thmath.SG
keywords complexcomponentdimensionstabilitytimesalternatingcaseconcrete
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abstract

We determine a full component of the space of stability conditions on $D^b(E^3)$ where $E$ is an elliptic curve without complex multiplication. The component has complex dimension 14 and a very concrete description in terms of alternating trilinear forms. This confirms a conjecture of Kontsevich, motivated by homological mirror symmetry, in the case of dimension $3$.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Stability conditions on threefolds

    math.AG 2026-07 accept novelty 7.0 of 10

    For a larger than an embedding-dependent bound a(X,H), restricted stability conditions on a threefold X coincide with the Bayer–Macrì–Toda double-tilt heart, proving the weak BMT inequality.

  2. Stability conditions and moduli spaces on projective families

    math.AG 2026-07 accept novelty 6.5 of 10

    Stability conditions exist on projective families over arbitrary bases and admit proper relative moduli spaces of semistable objects.

  3. A note on stability conditions on projective spaces

    math.AG 2026-07 accept novelty 4.0 of 10

    A new proof of Li's theorem on geometric Bridgeland stability conditions on projective spaces is given via quotient stack restriction.

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