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Inequalities for Hilbert functions and primary decompositions. (English. Russian original) Zbl 1206.13022

St. Petersbg. Math. J. 19, No. 6, 975-994 (2008); translation from Algebra Anal. 19, No. 6, 143-172 (2007); correction Algebra Anal. 20, No. 3, 245 (2008).
Summary: Upper bounds are found for the characteristic function of a homogeneous polynomial ideal \( I\); such estimates were previously known only for a radical ideal \( I\). An analog of the first Bertini theorem for primary decompositions is formulated and proved. Also, a new representation for primary ideals and modules is introduced and used, which is convenient from an algorithmic point of view.

MSC:

13D40 Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
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