Skip to content
DraconiticResearch
Search Sources API
201,818 studies31 sourcesUpdated 47 min ago
PreprintarXiv licencearXiv

Two-sided bounds for canonical traces of Veronese subalgebras

  • Sora Miyashita
Open at sourcePDFDOICite

Abstract

The classical Veronese formula of Goto--Watanabe identifies the canonical module of a Veronese subalgebra with the corresponding Veronese module. We prove the analogous compatibility for graded duals under a module-finite extension whose upper ring is equidimensional, satisfies Serre's condition (S2), and has dimension at least two, and obtain the formula for the b-invariant. This yields explicit two-sided bounds for canonical traces: the lower bound is controlled by the Loewy length of the canonical-trace quotient, whereas the upper bound is governed by the a- and b-invariants, with an S2-ification refinement for unmixed rings. We also characterize when all sufficiently large Veronese subalgebras of standard graded level algebras are nearly Gorenstein when the a-invariant is negative. Applications include Segre products, Stanley--Reisner rings and determinantal rings.

Related

  1. Traces of powers of canonical ideals
    Le Truong Hoang, Naoyuki Matsuoka
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Computing Smooth Geodesics under Two-Sided Curvature Bounds with Applications to Robotics and Image Analysis
    Da Chen, Zhenjiang Li, Jean-Marie Mirebeau +4
    HALPreprintLicence not statedNumerical analysis & scientific computingHAL
  3. Polynomial-in-r bounds for forbidden traces of uniform hypergraphs
    Pei Wu
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
  4. Matrix concentration inequalities and free probability II: Two-sided bounds and applications
    Afonso S. Bandeira, Giorgio Cipolloni, Dominik Schröder +1
    Communications of the American Mathematical SocietyPeer-reviewedCC BY-NC-ND33 citedStatisticsOpenAlex
  5. Sharp two-sided bounds for the product of modified Bessel functions and for its logarithmic derivative
    Javier Segura, Soichiro Suzuki
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{miyashita2026twosided,
  title = {{Two-sided bounds for canonical traces of Veronese subalgebras}},
  author = {Sora Miyashita},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.27782},
  eprint = {2609.27782},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27782},
}
RIS
TY  - UNPB
TI  - Two-sided bounds for canonical traces of Veronese subalgebras
AU  - Sora Miyashita
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.27782
UR  - https://arxiv.org/abs/2609.27782
AB  - The classical Veronese formula of Goto--Watanabe identifies the canonical module of a Veronese subalgebra with the corresponding Veronese module. We prove the analogous compatibility for graded duals under a module-finite extension whose upper ring is equidimensional, satisfies Serre's condition (S_2), and has dimension at least two, and obtain the formula for the b-invariant. This yields explicit two-sided bounds for canonical traces: the lower bound is controlled by the Loewy length of the canonical-trace quotient, whereas the upper bound is governed by the a- and b-invariants, with an S_2-ification refinement for unmixed rings. We also characterize when all sufficiently large Veronese subalgebras of standard graded level algebras are nearly Gorenstein when the a-invariant is negative. Applications include Segre products, Stanley--Reisner rings and determinantal rings.
ER  -