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math.AC2026
Weakly Newton-nondegenerate binomial ideals
Takayuki Hibi, Vinh Anh Pham
An ideal of a polynomial ring is called weakly Newton-nondegenerate, or weakly NND, if its integral closure is a monomial ideal. We study we…
math.AC2026
Transcendental Hilbert-Kunz Multiplicities
Sudipta Das, Stephen Landsittel, Vinh Anh Pham
We prove that ordinary Hilbert-Kunz multiplicity can be transcendental. More precisely, over every uncountable algebraically closed field of characteristic , there exists a no…
math.AC2026
Transcendental Epsilon Multiplicity via Divisor Volumes
Sudipta Das, Stephen Landsittel, Vinh Anh Pham
We prove that epsilon multiplicity can take transcendental values. The main structural result is a one-ideal formula for section rings: under natural positivity hypotheses, the eps…