ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Vol. LXXII, 1(2003)
p. 15 – 22
On Standard Basis and Multiplicity of (Xa – Yb, Xc – Yd)
E. Boda and R. Farnbauer
Abstract.
Let $I=(X^{a}-Y^{b},X^{c}-Y^{d})\cdot k[X,Y]$ be an ideal of
dimension zero in polynomial
ring in two variables. In this note a formula for standard basis of $I$
with respect of anti-graded lexicographic order is derived. As
a consequence the discussion on the common points of the plane
curves $V(X^{a}-Y^{b})$ and $V(X^{c}-Y^{d})$ is given.
AMS subject classification:
13H15, Secondary 13P10
Keywords:
Standard basis of ideal, local intersection multiplicity, Bezout Theorem
invariance
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