Hilbert-Kunz Functions of Binomial Hypersurfaces
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2002
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In this article, by making use of Gr¨obner basis, we determine the Hilbert-Kunz function of binomial hypersurfaces of the form f := Xa1 1 · · ·Xar r Y b1 1 · · · Y bs s + Y c1 1 · · · Y cs s Zd1 1 · · ·Zdt t which is HKR(n) = p(r+s+t−1)n + r+s+t−2 Xk=0 fk(n)pkn for n 0, where is a rational number and fk(n) is an eventually periodic function of n for each k. Moreover, we also determine the leading coecient . i
In this article, by making use of Gr¨obner basis, we determine the Hilbert-Kunz function of binomial hypersurfaces of the form f := Xa1 1 · · ·Xar r Y b1 1 · · · Y bs s + Y c1 1 · · · Y cs s Zd1 1 · · ·Zdt t which is HKR(n) = p(r+s+t−1)n + r+s+t−2 Xk=0 fk(n)pkn for n 0, where is a rational number and fk(n) is an eventually periodic function of n for each k. Moreover, we also determine the leading coecient . i
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Hilbert-Kunz