Let $(R,\germ m)$(R,m) be a Noetherian local ring and let $I$I and $J$J be $\germ m$m-primary ideals. Then the length of $R/I^{i}J^{j}$R/IiJj is a polynomial in $i$i and $j$j, for sufficiently large values of $i$i and $j$j. This is a classical result of P. B. Bhattacharya, generalizing the Hilbert-Samuel polynomial to the multi-ideal case. In this work, we extend some well-known results about the coefficients of the Hilbert polynomial to the analogous Bhattachrya polynomial.
Multigraded Hilbert coefficients
GUERRIERI, ANNA;
2005-01-01
Abstract
Let $(R,\germ m)$(R,m) be a Noetherian local ring and let $I$I and $J$J be $\germ m$m-primary ideals. Then the length of $R/I^{i}J^{j}$R/IiJj is a polynomial in $i$i and $j$j, for sufficiently large values of $i$i and $j$j. This is a classical result of P. B. Bhattacharya, generalizing the Hilbert-Samuel polynomial to the multi-ideal case. In this work, we extend some well-known results about the coefficients of the Hilbert polynomial to the analogous Bhattachrya polynomial.File in questo prodotto:
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