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Let I be a homogeneous ideal of $$S=K[x_1,\ldots , x_n]$$ and let J be an initial ideal of I with respect to a term order. We prove that if J… Click to show full abstract
Let I be a homogeneous ideal of $$S=K[x_1,\ldots , x_n]$$ and let J be an initial ideal of I with respect to a term order. We prove that if J is radical then the Hilbert functions of the local cohomology modules supported at the homogeneous maximal ideal of S/I and S/J coincide. In particular, $${\text {depth}} (S/I)={\text {depth}} (S/J)$$ and $${\text {reg}} (S/I)={\text {reg}} (S/J)$$.
Keywords:
bner degenerations;
text;
square free;
free bner
Journal Title: Inventiones Mathematicae
Year Published: 2020
Link to full text (if available)
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Journal Title: Inventiones Mathematicae
Year Published: 2020
Link to full text (if available)
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recommendations!