Regularity Bounds for Space Curves by Minimal Generators and Hilbert Function
نویسندگان
چکیده
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 for a curve C providing several examples.
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 ...
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