Regularity bounds by minimal generators and Hilbert function
نویسندگان
چکیده
منابع مشابه
Regularity Bounds for Curves by Minimal Generators and Hilbert Function
Let ρC be the regularity of the Hilbert function of a projective curve C in P K over an algebraically closed field K and α1, . . . , αn−1 be minimal degrees for which there exists a complete intersection of type (α1, . . . , αn−1) containing the curve C. Then the Castelnuovo-Mumford regularity of C is upper bounded by max{ρC +1, α1 + . . .+αn−1 − (n− 2)}. We study and, for space curves, refine ...
متن کاملRegularity Bounds for Space Curves by Minimal Generators and Hilbert Function
Let ρC be the regularity of the Hilbert function of a projective space curve C over an algebraically closed field, αI be the initial degree of the defining ideal I of C and βI the least degree t such that the depth of the ideal generated by I≤t is depth(I). Then the Castelnuovo-Mumford regularity reg(C) of C is upper bounded by max{ρC +1, αI +βI −1}. We study in deep and refine the above bound ...
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Article history: Received 4 April 2008 Available online 18 December 2008 Communicated by Stewen Dale Cutkosky
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Bounds for the Castelnuovo-Mumford regularity and Hilbert coefficients are given in terms of the arithmetic degree (if the ring is reduced) or in terms of the defining degrees. From this it follows that there exists only a finite number of Hilbert functions associated with reduced algebras over an algebraically closed field with a given arithmetic degree and dimension. A good bound is also give...
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ژورنال
عنوان ژورنال: Collectanea mathematica
سال: 2009
ISSN: 0010-0757
DOI: 10.1007/bf03191218