Higher iterated Hilbert coefficients of the graded components of bigraded modules

Seyed Shahab Arkian

Higher iterated Hilbert coefficients of the graded components of bigraded modules

Commutative Algebra 2016-10-11 v1

Authors: Seyed Shahab Arkian

Abstract

Let $S=K[x_1,\ldots,x_n]$ be the polynomial ring over the field $K$ , and let $I\subset S$ be a graded ideal. It is shown that the higher iterated Hilbert coefficients of the graded $S$ -modules $\Tor_i^S(M,I^k)$ and $\Ext^i_S(M,I^k)$ are polynomial functions in $k$ , and an upper bound for their degree is given. These results are derived by considering suitable bigraded modules.

Keywords

Hilbert coefficients bigraded modules Tor functor Ext functor graded ideal polynomial ring

Cite

@article{arxiv.1610.02655,
  title  = {Higher iterated Hilbert coefficients of the graded components of bigraded modules},
  author = {Seyed Shahab Arkian},
  journal= {arXiv preprint arXiv:1610.02655},
  year   = {2016}
}

Comments

10 pages

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