4 papers
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…
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…
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…
Multiplicity Volume formula and Newton non-degenerate ideals in regular local rings
Tài Huy Hà, Thai Thanh Nguyen, Vinh Anh Pham
We develop the notions of Newton non-degenerate (NND) ideals and Newton polyhedra for regular local rings. These concepts were first defined in the context of complex analysis. We…