Let <i>f</i><subscrpt>1</subscrpt>,…,<i>f<subscrpt>n</subscrpt></i> be homogeneous polynomials generating a generic ideal <i>I</i> in the ring of polynomials in <i>n</i> variables over an infinite field. Moreno-Socías conjectured that for the graded reverse lexicographic term ordering, the initial ideal in(<i>I</i>) is a weakly reverse lexicographic ideal. This paper contains a new proof of Moreno-Socías' conjecture for the case <i>n</i> = 2.
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