2 problems

Let $S$ be a graded polynomial ring and let $I\subset S$ be a homogeneous ideal. Write $\operatorname{gin}(I)$ for the generic initial ideal of $I$. The homological degree comparis…

Let $S$ be the graded polynomial ring and let $M$ be a finitely generated graded $S$-module. For an element $y\in S$ that is $M$-regular, consider the quotient $M/yM$. Vasconcelos'…