Cheng Meng

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20212026

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4 papers · 2 filters

math.AC2025

Finiteness and infiniteness of gradings of Noetherian rings

Cheng Meng

In this paper we show that for a torsion-free abelian group $G$ , $rank_{Z} G < \infty$ if and only if there exists a Noetherian $G$ -graded ring $R$ such that the…

math.AC2025

Explicit Stillman bounds for all degrees

Giulio Caviglia, Yihui Liang, Cheng Meng

In 2016 Ananyan and Hochster proved Stillman's conjecture by showing the existence of a uniform upper bound on the length of an $R_{η}$ -sequence containing fixed $n$ forms of degree…

math.AC2025

Limits of $F$ -invariants and Riemann-Stieltjes integral

Cheng Meng

This paper proves several results on $F$ -invariants of Fermat hypersurfaces, including the proof of an inequality on the Hilbert-Kunz multiplicity of Fermat quadric hypersurfaces c…

math.AC2025

Restrictions on Hilbert coefficients give depths of graded domains

Cheng Meng

In this paper, we prove that if $P$ is a homogeneous prime ideal inside a standard graded polynomial ring $S$ with $dim (S / P) = d$ , and for $s \leq d$ , adjoining $s$ general linear f…

Finiteness and infiniteness of gradings of Noetherian rings

Explicit Stillman bounds for all degrees

Limits of F-invariants and Riemann-Stieltjes integral

Restrictions on Hilbert coefficients give depths of graded domains

Limits of $F$ -invariants and Riemann-Stieltjes integral