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[[alternative]]Hilbert-Kunz Functions of Plane Conic And Cubic Curves

By [[author]]王志傑 and 王志傑


[[abstract]]Let k be an algebraic closed field, is the polynomial ring, q is a power of the characteristic p of the field k. If is a homogeneous form, then we define the Hilbert-Kunz function of to be the dimension of the vector space . In this article, I classify the various cases of the projective conic and cubic plane curves, and determine their Hilbert-Kunz functions mainly by means of Gr?ebner bases. Some cubic cases are more complicated, so another strategy is applied.

Topics: 希爾伯特方程式, Hilbert-Kunz functions, plane curves, [[classification]]37
Year: 2010
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