Pith Number

pith:Z5EN3TWC

pith:2026:Z5EN3TWCFARSKCFP5AAHOYKJZ2

not attested not anchored not stored refs resolved

Homological Mirror Symmetry for Conic Bundle

Bohan Fang, Peng Zhou, Yuze Sun

For the conic bundle mirror of a toric Fano orbifold's canonical bundle, the wrapped microlocal sheaf category on the skeleton equals the coherent sheaves on the space minus its anti-canonical divisor.

arxiv:2605.16040 v1 · 2026-05-15 · math.AG · math.SG

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\pithnumber{Z5EN3TWCFARSKCFP5AAHOYKJZ2}

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4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

When X is the canonical bundle of a toric Fano n-orbifold S and f is its Givental superpotential, the strong deformation retraction skeleton L of Y has a Weinstein neighborhood U such that the wrapped microlocal sheaf category μSh^w_L(L) ≅ Coh(X^∘). This proves a microlocal categorical version of the SYZ mirror.

C2weakest assumption

The paper assumes that the skeleton L from the RSTZ construction admits a Weinstein neighborhood U in which the wrapped microlocal sheaf category can be defined and that the specific choice of f as the Givental superpotential ensures the isomorphism holds, as stated in the conditions for the equivalence.

C3one line summary

Proves that the wrapped microlocal sheaf category μSh^w_L(L) is equivalent to Coh(X^∘) for conic bundle mirrors of toric Calabi-Yau (n+2)-folds under given conditions.

References

34 extracted · 34 resolved · 0 Pith anchors

[1] Publications math

[2] and Chen, Linda and Smith, Gregory G

[3] International Mathematics Research Notices , volume =

[4] 2025 , eprint = 2025 · doi:10.48550/arxiv.2504.15696

[5] Gammage, Benjamin and Le, Ian , title =. SIGMA. Symmetry, Integrability and Geometry: Methods and Applications , volume =

Receipt and verification

First computed	2026-05-20T00:01:50.351517Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf48ddcec228232508afe800776149ceb915ed1029bb5f161b396ba8088b9baa

Aliases

arxiv: 2605.16040 · arxiv_version: 2605.16040v1 · doi: 10.48550/arxiv.2605.16040 · pith_short_12: Z5EN3TWCFARS · pith_short_16: Z5EN3TWCFARSKCFP · pith_short_8: Z5EN3TWC

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/Z5EN3TWCFARSKCFP5AAHOYKJZ2 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: cf48ddcec228232508afe800776149ceb915ed1029bb5f161b396ba8088b9baa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36e4c11dae051fe4a4a82f3da0ba322d04562d328e2b6f97c9ba4d400f477432",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-05-15T15:13:56Z",
    "title_canon_sha256": "b15eb64559bc0cbb1b88f2db3f951a896037a93661f7b4584cd0fab1c92dff67"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16040",
    "kind": "arxiv",
    "version": 1
  }
}