The Euler-Poincaré Characteristic and Mixed Multiplicities

Việt, Duong Quôc; Thanh, Truong Thi Hong

doi:10.2206/kyushujm.69.393

Cited by 2 publications

(1 citation statement)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Filter-regular sequences are related to superficial sequences and (mixed) multiplicity systems, and are widely used in the study of Rees algebras and Hilbert functions of local rings. See for example [TV10], [RV10], [VT15] or [KR94].…”

Section: Contentsmentioning

confidence: 99%

Multigraded Koszul complexes, filter-regular sequences and lower bounds for the multiplicity of the resultant

Ghidelli

2019

Preprint

View full text Add to dashboard Cite

The Rémond resultant attached to a multiprojective variety and a sequence of multihomogeneous polynomials is a polynomial form in the coefficients of the polynomials, which vanishes if and only if the polynomials have a common zero on the variety. We demonstrate that this resultant can be computed as a Cayley determinant of a multigraded Koszul complex, proving a key stabilization property with the aid of local Hilbert functions and the notion of filter-regular sequences. Then we prove that the Rémond resultant vanishes, under suitable hypotheses, with order at least equal to the number of common zeros of the polynomials. More generally, we estimate the multiplicity of resultants of multihomogeneous polynomials along prime ideals of the coefficient ring, thus considering for example the order of p-adic vanishing. Finally, we exhibit a corollary of this multiplicity estimate in the context of interpolation on commutative algebraic groups, with applications to Transcendental Number Theory.

show abstract

Section: Contentsmentioning

confidence: 99%

Multigraded Koszul complexes, filter-regular sequences and lower bounds for the multiplicity of the resultant

Ghidelli

2019

Preprint

View full text Add to dashboard Cite

show abstract

The Euler–Poincaré characteristic of joint reductions and mixed multiplicities

Thanh

Việt

2020

J. Algebra Appl.

View full text Add to dashboard Cite

This paper defines the Euler–Poincaré characteristic of joint reductions of ideals which concerns the maximal terms in the Hilbert polynomial; characterizes the positivity of mixed multiplicities in terms of minimal joint reductions; proves the additivity and other elementary properties for mixed multiplicities. The results of the paper together with the results of [Thanh and Viet, Mixed multiplicities of maximal degrees, J. Korean Math. Soc. 55(3) (2018) 605–622] seem to show a natural and nice picture of mixed multiplicities of maximal degrees.

show abstract

The Euler-Poincaré Characteristic and Mixed Multiplicities

Cited by 2 publications

References 29 publications

Multigraded Koszul complexes, filter-regular sequences and lower bounds for the multiplicity of the resultant

Multigraded Koszul complexes, filter-regular sequences and lower bounds for the multiplicity of the resultant

The Euler–Poincaré characteristic of joint reductions and mixed multiplicities

Contact Info

Product

Resources

About