منابع مشابه
Toric Ideals for High Veronese Subrings of Toric Algebras
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...
متن کاملInitial 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...
متن کاملOn the Log-concavity of Hilbert Series of Veronese Subrings and Ehrhart Series
For every positive integer n, consider the linear operator Un on polynomials of degree at most d with integer coefficients defined as follows: if we write h(t) (1−t)d+1 = P m≥0 g(m) t , for some polynomial g(m) with rational coefficients, then Un h(t) (1−t)d+1 = P m≥0 g(nm) t . We show that there exists a positive integer nd, depending only on d, such that if h(t) is a polynomial of degree at m...
متن کاملTight Closure and Differential Simplicity
The behavior of the Hasse–Schmidt algebra under étale extension is used to show that the Hasse–Schmidt algebra of a smooth algebra of finite type over a field equals the ring of differential operators. These techniques show that the formation of Hasse–Schmidt derivations does not commute with localization, providing a counterexample to a question of Brown and Kuan; their conjecture is reformula...
متن کاملTight Closure and Projective Bundles
We formulate problems of tight closure theory in terms of projective bundles and subbundles. This provides a geometric interpretation of such problems and allows us to apply intersection theory to them. This yields new results concerning the tight closure of a primary ideal in a two-dimensional graded domain.
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2000
ISSN: 0030-8730
DOI: 10.2140/pjm.2000.192.399