Pith Number

pith:3T6UPOJE

pith:2026:3T6UPOJEVEBYLGDQVCYEFK7YC5

not attested not anchored not stored refs resolved

On the DCC Property of Iitaka Volume with Real Coefficients and Generalised Pairs

Pinxian Bie

The set of Iitaka volumes for pairs of varieties satisfies the descending chain condition with real coefficients.

arxiv:2605.13881 v1 · 2026-05-11 · math.AG

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\pithnumber{3T6UPOJEVEBYLGDQVCYEFK7YC5}

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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

The set of Iitaka volumes of a given set of pairs of varieties satisfies the DCC property; this generalizes previous results of Birkar and Li about usual pairs to the real coefficient case and establishes similar results on generalised pairs under natural boundedness assumptions.

C2weakest assumption

Natural boundedness assumptions are required for technical reasons when treating generalised pairs.

C3one line summary

The DCC property for Iitaka volumes holds for real-coefficient pairs and for generalized pairs with natural boundedness assumptions.

References

32 extracted · 32 resolved · 1 Pith anchors

[1] The Adjunction Conjecture and its applications 1999 · arXiv:math/9903060

[2] Florin Ambro, The moduli b -divisor of an lc-trivial fibration , Compos. Math. 141 (2005), no. 2, 385--403 2005

[3] C. Birkar, P. Cascini, C. D. Hacon, and J. McKernan, Existence of minimal models for varieties of log general type , J. Amer. Math. Soc. 23 (2010), no. 2, 405--468 2010

[4] C. Birkar and C. D. Hacon, Variations of generalised pairs, arXiv:2204.10456 (2022) 2022

[5] Birkar, Existence of log canonical flips and a special LMMP , Pub 2012

Receipt and verification

First computed	2026-05-17T23:39:19.184375Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dcfd47b924a903859870a8b042abf8174e8bf9f77a413b4a6c9ee8a0362eca01

Aliases

arxiv: 2605.13881 · arxiv_version: 2605.13881v1 · doi: 10.48550/arxiv.2605.13881 · pith_short_12: 3T6UPOJEVEBY · pith_short_16: 3T6UPOJEVEBYLGDQ · pith_short_8: 3T6UPOJE

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/3T6UPOJEVEBYLGDQVCYEFK7YC5 \
  | 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: dcfd47b924a903859870a8b042abf8174e8bf9f77a413b4a6c9ee8a0362eca01

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "852902dd17d30470dc5c8fb3185cb2d311566bb0461b7f612b4a90bfc6d19164",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-05-11T06:01:42Z",
    "title_canon_sha256": "4897dc7e13f016f6f2a69701c92a26ca97c06ecc472319a8ccf1b0a8d8a15b1f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13881",
    "kind": "arxiv",
    "version": 1
  }
}