Hilbert polynomials of non-standard bigraded algebras
Commutative Algebra
2007-05-23 v1 Algebraic Geometry
Abstract
This paper is a systematic study of the Hilbert polynomial of a bigraded algebra R which are generated by elements of bidegrees (1,0), (d_1,1),...,(d_r,1), where d_1,...,d_r are non-negative integers. The obtained results can be applied to study Rees algebras of homogeneous ideals and their diagonal subalgebras. The Hilbert polynomial is computed explicitly in the following cases: (1) R is a bigraded polynomial ring of the above type; (2) R is the Rees algebra of an ideal generated by a homogeneous regular sequence; (3) R is the Rees algebra of the ideal generated by the maximal minors of a generic (r-1) by r matrix.
Cite
@article{arxiv.math/0211181,
title = {Hilbert polynomials of non-standard bigraded algebras},
author = {Nguyen Duc Hoang and Ngo Viet Trung},
journal= {arXiv preprint arXiv:math/0211181},
year = {2007}
}
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23 pages