Equidimensional and Unmixed Ideals of Veronese Type
نویسندگان
چکیده
منابع مشابه
Equidimensional and Unmixed Ideals of Veronese Type
This paper was motivated by a problem left by Herzog and Hibi, namely to classify all unmixed polymatroidal ideals. In the particular case of polymatroidal ideals corresponding to discrete polymatroids of Veronese type, i.e ideals of Veronese type, we give a complete description of the associated prime ideals and then, we show that such an ideal is unmixed if and only if it is CohenMacaulay. We...
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In this paper, we present a modular strategy which describes key properties of the absolute primary decomposition of an equidimensional polynomial ideal defined by polynomials with rational coefficients. The algorithm we design is based on the classical technique of elimination of variables and colon ideals and uses a tricky choice of prime integers to work with. Thanks to this technique, we ca...
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چکیده ندارد.
Initial ideals, Veronese subrings, and rates of algebras
Let S be a polynomial ring over an infinite field and let I be a homogeneous ideal of S. Let Td be a polynomial ring whose variables correspond to the monomials of degree d in S. We study the initial ideals of the ideals Vd(I) ⊂ Td that define the Veronese subrings of S/I. In suitable orders, they are easily deduced from the initial ideal of I. We show that in(Vd(I)) is generated in degree ≤ ma...
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We prove that the defining ideal of a sufficiently high Veronese subring of a toric algebra admits a quadratic Gröbner basis consisting of binomials. More generally, we prove that the defining ideal of a sufficiently high Veronese subring of a standard graded ring admits a quadratic Gröbner basis. This was proved by Eisenbud–Reeves–Totaro in the case where coordinates are generic. Our proof doe...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2008
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927870802107595