Monomial ideals with tiny squares
Abstract
Let I ⊂ K[x,y] be a monomial ideal. How small can μ(I2) be in terms of μ(I)? It has been expected that the inequality μ(I2) > μ(I) should hold whenever μ(I) 2. Here we disprove this expectation and provide a somewhat surprising answer to the above question.
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