ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. LXXII, 1(2003)
p. 15 – 22

On Standard Basis and Multiplicity of (XaYb, XcYd)
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