Pith Number

pith:MFHNYNCB

pith:2026:MFHNYNCBWHNGKD46ARCVNBYA2C

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Support theorem of universal compactified Jacobians

Yifan Wu

Every summand in the decomposition of the pushforward of the intersection cohomology sheaf from the universal compactified Jacobian has full support over the moduli space of curves.

arxiv:2605.03097 v2 · 2026-05-04 · math.AG

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Claims

C1strongest claim

We prove a full support theorem for the relative good moduli space of the universal compactified Jacobian π̄ : J̄_{g,n}^{d,φ} → M̄_{g,n}, showing that every direct summand appearing in the BBDG decomposition of Rπ̄_* IC(J̄_{g,n}^{d,φ}) has full support on the base M̄_{g,n}.

C2weakest assumption

The stability condition φ and degree d are chosen so that the good moduli space morphism exists and the intersection cohomology sheaf behaves well under the cited decomposition and support theorems; the abstract does not specify the precise range of (g,n,d,φ) for which this holds.

C3one line summary

Every direct summand in the BBDG decomposition of Rπ_* IC of the universal compactified Jacobian has full support on the base moduli space of curves, with the decomposition governed by the pushforward of the constant sheaf on the universal curve.

Receipt and verification

First computed	2026-06-02T02:04:18.482606Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

614edc3441b1da650f9e0445568700d0a56e9e24c3f935cc2333bbf03c8d4029

Aliases

arxiv: 2605.03097 · arxiv_version: 2605.03097v2 · doi: 10.48550/arxiv.2605.03097 · pith_short_12: MFHNYNCBWHNG · pith_short_16: MFHNYNCBWHNGKD46 · pith_short_8: MFHNYNCB

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/MFHNYNCBWHNGKD46ARCVNBYA2C \
  | 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: 614edc3441b1da650f9e0445568700d0a56e9e24c3f935cc2333bbf03c8d4029

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74e7bb871f6d05cdc01c14fa3081f3ec7153ec4df69afdeda20483a46ce46481",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-05-04T19:25:23Z",
    "title_canon_sha256": "eede5c57951030597e67e4cfb80e23f2756d3d23c5d8da5ef3336c23d480cc55"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.03097",
    "kind": "arxiv",
    "version": 2
  }
}