Mixed multiplicities and the multiplicity of Rees modules of reductions

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.

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Mixed multiplicities and the multiplicity of Rees modules of reductions

Abstract: This paper shows that mixed multiplicities and the multiplicity of Rees modules of good filtrations and that of their reductions are the same. As an application of this result, we obtain interesting results on mixed multiplicities and the multiplicity of Rees modules.

Cited by 2 publications

References 26 publications

Toward Mixed Multiplicities and Joint Reductions

Toward Mixed Multiplicities and Joint Reductions

The Euler–Poincaré characteristic of joint reductions and mixed multiplicities

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