Pith Number

pith:J5QCI7WM

pith:2026:J5QCI7WMCS6GYHBY37LBFLFNL4

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Tautological modular forms of level two and degree two

Fabien Cl\'ery, Gerard van der Geer

Divisors on the projectivized Hodge bundle generate all vector-valued Siegel modular forms of level two and degree two.

arxiv:2605.13300 v1 · 2026-05-13 · math.AG · math.NT

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications 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

We construct all vector-valued Siegel modular forms of level two and degree two in terms of certain basic modular forms that are intimately connected to the moduli of curves of genus two.

C2weakest assumption

That the divisors on the projectivized Hodge bundle produce a complete set of generators under the action of invariant theory without missing relations or requiring additional ad-hoc forms.

C3one line summary

All vector-valued Siegel modular forms of level two and degree two are generated from basic forms connected to genus-two curve moduli via divisors on the projectivized Hodge bundle and invariant theory.

References

21 extracted · 21 resolved · 0 Pith anchors

[1] J. Bergstr¨ om, F. Cl´ ery:Dimension formulas for spaces of vector-valued Siegel modular forms of degree2and level2.Publ. Mat.,69(2), 367—388, 2025 2025

[2] J. Bruinier, G. van der Geer, G. Harder, D. Zagier:The 1-2-3 of modular forms.Universitext. Springer Verlag 2007 2007

[3] F. Cl´ ery, C. Faber, and G. van der Geer:Covariants of binary sextics and vector-valued Siegel modular forms of genus2.Math. Annalen369(3—4), 1649—1669 (2017) 2017

[4] F. Cl´ ery, C. Faber, and G. van der Geer:Covariants of binary sextics and modular forms of degree 2with a character.Mathematics of Computation88, No. 319, 2423–2441, 2019 2019

[5] F. Cl´ ery, C. Faber, and G. van der Geer:Concomitants of ternary quartics and vector-valued Siegel modular and Teichmueller modular forms of genus three.Selecta Mathematica (2020) 26:55 2020

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:49.051021Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f60247ecc14bc6c1c38dfd612acad5f3f5024230295789db5fac40b91726e42

Aliases

arxiv: 2605.13300 · arxiv_version: 2605.13300v1 · doi: 10.48550/arxiv.2605.13300 · pith_short_12: J5QCI7WMCS6G · pith_short_16: J5QCI7WMCS6GYHBY · pith_short_8: J5QCI7WM

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/J5QCI7WMCS6GYHBY37LBFLFNL4 \
  | 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: 4f60247ecc14bc6c1c38dfd612acad5f3f5024230295789db5fac40b91726e42

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f9bdbfe5a89e286635ee720d41cf7b00a54b1c69e062ca799b8aa67c09500bc3",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-05-13T10:13:21Z",
    "title_canon_sha256": "f8e151a4cc3298fa04e5c2c5890703002bfe0151801a84062cf7c8b7ab01e86c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13300",
    "kind": "arxiv",
    "version": 1
  }
}