Pith Number

pith:NERKIO4Q

pith:2025:NERKIO4QQJXGI2O6KTWOSPKV5O

not attested not anchored not stored refs pending

Abelian varieties analogs of two results about algebraic curves

Giuseppe Pareschi, Nelson Alvarado

Decomposable principally polarized abelian varieties of the form E×B are identified by failures in normal generation and second-order Gaussian map surjectivity, in direct analogy to hyperelliptic curves.

arxiv:2502.11288 v4 · 2025-02-16 · math.AG

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\pithnumber{NERKIO4QQJXGI2O6KTWOSPKV5O}

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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

We characterize decomposable principally polarized abelian varieties of the form E×B, with E an elliptic curve, in two different ways, which are, surprisingly, completely analogous to classical results of curve theory concerning hyperelliptic curves.

C2weakest assumption

The assumption that the normal generation property and the surjectivity of Gaussian maps fail precisely for these decomposable varieties, relying on the specific choice of the polarization Θ and the equivalence to Nakamaye's theorem.

C3one line summary

Characterizes decomposable p.p.a.v.s E×B via failure of normal generation of a module over Sym H^0(2Θ) and via non-surjectivity of second-order Gaussian maps for 6Θ (equiv. 3Θ fails to separate 2-jets), plus equivalence to effective Nakamaye theorem on minimal Seshadri constant.

Receipt and verification

First computed	2026-06-09T02:07:02.199280Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6922a43b90826e6469de54ece93d55eba802ffdeefab48213849932a86ddd59a

Aliases

arxiv: 2502.11288 · arxiv_version: 2502.11288v4 · doi: 10.48550/arxiv.2502.11288 · pith_short_12: NERKIO4QQJXG · pith_short_16: NERKIO4QQJXGI2O6 · pith_short_8: NERKIO4Q

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/NERKIO4QQJXGI2O6KTWOSPKV5O \
  | 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: 6922a43b90826e6469de54ece93d55eba802ffdeefab48213849932a86ddd59a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72f7abc539077605ce56309967cc42d06a0696e506c6f4eed089318b60fb4b0b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2025-02-16T22:21:55Z",
    "title_canon_sha256": "04acee0b4bb5dfbb010daeb3d0aca9270dda1101da8961b46a569243dd1ae2c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.11288",
    "kind": "arxiv",
    "version": 4
  }
}