Depth of some square free monomial ideals

الأصل · EN

Let I J be two square free monomial ideals of a polynomial algebra over a field generated in degree ≥ 1, resp. ≥ 2. Almost always when I contains precisely one variable, the other generators having degrees ≥ 2, if the Stanley depth of I/J is ≤ 2 then the usual depth of I/J is ≤ 2 too, that is the Stanley Conjecture holds in these cases.