8 papers · 1 filter
Limits of -invariants and Riemann-Stieltjes integral
Cheng Meng
This paper proves several results on -invariants of Fermat hypersurfaces, including the proof of an inequality on the Hilbert-Kunz multiplicity of Fermat quadric hypersurfaces c…
Hilbert-Kunz multiplicity of quadrics decreases
Cheng Meng
In this paper we prove that the Green ring of is the -fold tensor product of the Green ring of , and this isomorphism is given…
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 -sequence containing fixed forms of degree…
Finiteness and infiniteness of gradings of Noetherian rings
Cheng Meng
In this paper we show that for a torsion-free abelian group , if and only if there exists a Noetherian -graded ring such that the…
-function, Hilbert-Kunz density function and Frobenius-Poincaré function
Cheng Meng, Alapan Mukhopadhyay
Given ideals of a noetherian local ring such that is -primary and a finitely generated -module , we associate an invariant of $(M,…
Strongly Lech-independent ideals and Lech's conjecture
Cheng Meng
We introduce the notion of strongly Lech-independent ideals as a generalization of Lech-independent ideals defined by Lech and Hanes, and use this notion to derive inequalities on…